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The eigenvalues of the matrix The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , are The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , and The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , . Find an eigenvector corresponding to each of the given eigenvalues.


A) The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , ; The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; ,
B) The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , ; The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; ,
C) The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , ; The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; ,
D) The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , ; The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; ,
E) The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , ; The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; , , The eigenvalues of the matrix are and . Find an eigenvector corresponding to each of the given eigenvalues. A) , ; , B) , ; , C) , ; , D) , ; , E) , ; ,

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Find Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , , and Find , and . , . A) , , B) , , C) , , D) , , E) , , . Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , , .


A) Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , ,
B) Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , ,
C) Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , ,
D) Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , ,
E) Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , , , Find , and . , . A) , , B) , , C) , , D) , , E) , ,

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Find the area of the triangle having the vertices Find the area of the triangle having the vertices , , and . A) 12 B) 6 C) 30 D) 69 E) 9 , Find the area of the triangle having the vertices , , and . A) 12 B) 6 C) 30 D) 69 E) 9 , and Find the area of the triangle having the vertices , , and . A) 12 B) 6 C) 30 D) 69 E) 9 .


A) 12
B) 6
C) 30
D) 69
E) 9

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Find the minor Find the minor and its cofactor of the matrix . A) B) C) D) E) and its cofactor Find the minor and its cofactor of the matrix . A) B) C) D) E) of the matrix Find the minor and its cofactor of the matrix . A) B) C) D) E) .


A) Find the minor and its cofactor of the matrix . A) B) C) D) E) Find the minor and its cofactor of the matrix . A) B) C) D) E)
B) Find the minor and its cofactor of the matrix . A) B) C) D) E) Find the minor and its cofactor of the matrix . A) B) C) D) E)
C) Find the minor and its cofactor of the matrix . A) B) C) D) E) Find the minor and its cofactor of the matrix . A) B) C) D) E)
D) Find the minor and its cofactor of the matrix . A) B) C) D) E) Find the minor and its cofactor of the matrix . A) B) C) D) E)
E) Find the minor and its cofactor of the matrix . A) B) C) D) E) Find the minor and its cofactor of the matrix . A) B) C) D) E)

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Determine whether the points Determine whether the points , , , and are coplanar. , Determine whether the points , , , and are coplanar. , Determine whether the points , , , and are coplanar. , and Determine whether the points , , , and are coplanar. are coplanar.

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Use Cramer's Rule to solve the system of equations Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) , .


A) Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) , , Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) ,
B) Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) , , Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) ,
C) Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) , , Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) ,
D) Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) , , Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) ,
E) Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) , , Use Cramer's Rule to solve the system of equations . A) , B) , C) , D) , E) ,

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Find the characteristic equation of the matrix Find the characteristic equation of the matrix . A) B) C) D) E) .


A) Find the characteristic equation of the matrix . A) B) C) D) E)
B) Find the characteristic equation of the matrix . A) B) C) D) E)
C) Find the characteristic equation of the matrix . A) B) C) D) E)
D) Find the characteristic equation of the matrix . A) B) C) D) E)
E) Find the characteristic equation of the matrix . A) B) C) D) E)

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Solve for x given the following equation involving a determinant. Solve for x given the following equation involving a determinant. A) B) C) D) E)


A) Solve for x given the following equation involving a determinant. A) B) C) D) E)
B) Solve for x given the following equation involving a determinant. A) B) C) D) E)
C) Solve for x given the following equation involving a determinant. A) B) C) D) E)
D) Solve for x given the following equation involving a determinant. A) B) C) D) E)
E) Solve for x given the following equation involving a determinant. A) B) C) D) E)

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C

Find the determinant of Find the determinant of by the method of expansion by cofactors. A) 192 B) 384 C) -48 D) -384 E) 176 by the method of expansion by cofactors.


A) 192
B) 384
C) -48
D) -384
E) 176

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Use the matrix capabilities of a graphing utility to find the determinant of the matrix Use the matrix capabilities of a graphing utility to find the determinant of the matrix . A) -162 B) 0 C) -216 D) -188 E) 188 .


A) -162
B) 0
C) -216
D) -188
E) 188

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E

Evaluate the determinant of the matrix below to determine which of the following makes the equation true. Evaluate the determinant of the matrix below to determine which of the following makes the equation true. A) B) C) D) E)


A) Evaluate the determinant of the matrix below to determine which of the following makes the equation true. A) B) C) D) E)
B) Evaluate the determinant of the matrix below to determine which of the following makes the equation true. A) B) C) D) E)
C) Evaluate the determinant of the matrix below to determine which of the following makes the equation true. A) B) C) D) E)
D) Evaluate the determinant of the matrix below to determine which of the following makes the equation true. A) B) C) D) E)
E) Evaluate the determinant of the matrix below to determine which of the following makes the equation true. A) B) C) D) E)

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Evaluate Evaluate for the matrix . A) 8 B) 784 C) -220 D) 4 E) 484 for the matrix Evaluate for the matrix . A) 8 B) 784 C) -220 D) 4 E) 484 .


A) 8
B) 784
C) -220
D) 4
E) 484

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D

Use elementary row or column operations to evaluate the determinant. Use elementary row or column operations to evaluate the determinant. A) 160 B) 0 C) -160 D) 120 E) -120


A) 160
B) 0
C) -160
D) 120
E) -120

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Find the volume of the tetrahedron having the vertices Find the volume of the tetrahedron having the vertices , , , and . A) 2 B) 12 C) 26 D) 4 E) 31 , Find the volume of the tetrahedron having the vertices , , , and . A) 2 B) 12 C) 26 D) 4 E) 31 , Find the volume of the tetrahedron having the vertices , , , and . A) 2 B) 12 C) 26 D) 4 E) 31 , and Find the volume of the tetrahedron having the vertices , , , and . A) 2 B) 12 C) 26 D) 4 E) 31 .


A) 2
B) 12
C) 26
D) 4
E) 31

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Use technology to find the determinant. Use technology to find the determinant. A) 119 B) -119 C) -207 D) -115 E) 121


A) 119
B) -119
C) -207
D) -115
E) 121

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Use Cramer's Rule to solve the following system of linear equations Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = .


A) x = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , y = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , z = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z =
B) x = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , y = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , z = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z =
C) x = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , y = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , z = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z =
D) x = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , y = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , z = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z =
E) x = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , y = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z = , z = Use Cramer's Rule to solve the following system of linear equations . A) x = , y = , z = B) x = , y = , z = C) x = , y = , z = D) x = , y = , z = E) x = , y = , z =

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Which property of determinants is illustrated by the equation Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c.


A) If every entry of an Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c. matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c.
B) If a single row or a single column of an Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c. matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c.
C) If a single row or a single column of an Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c. matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c. .
D) If every entry of an Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c. matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c.
E) If c times one row is added to another row of an Which property of determinants is illustrated by the equation A) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. B) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. C) If a single row or a single column of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by . D) If every entry of an matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by E) If c times one row is added to another row of an matrix, the determinant of the matrix is multiplied by c. matrix, the determinant of the matrix is multiplied by c.

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Use the fact that for an Use the fact that for an matrix A, , to evaluate . A) -420 B) -1,050 C) -26,250 D) 1,050 E) 26,250 matrix A, Use the fact that for an matrix A, , to evaluate . A) -420 B) -1,050 C) -26,250 D) 1,050 E) 26,250 , to evaluate Use the fact that for an matrix A, , to evaluate . A) -420 B) -1,050 C) -26,250 D) 1,050 E) 26,250 .


A) -420
B) -1,050
C) -26,250
D) 1,050
E) 26,250

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Use the determinant to decide whether the matrix given below is singular or nonsingular. Use the determinant to decide whether the matrix given below is singular or nonsingular. A) nonsingular B) singular


A) nonsingular
B) singular

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Find the determinant of the elementary matrix Find the determinant of the elementary matrix . A) 1 B) 1- k C) k D) -k E) k - 1 .


A) 1
B) 1- k
C) k
D) -k
E) k - 1

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