Matrices and Their Inverses — Quiz Answers

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1
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A square matrix that does not have an inverse is most specifically called a(n):

A
inverse matrix
B
identity matrix
C
singular matrix
D
non-singular matrix
2
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Which of the following represents the inverse of the matrix? cap A is equal to the 2 by 2 matrix row 1, A b row 2, c d

A
the fraction with numerator 1 and denominator absolute value of cap A the 2 by 2 matrix, row 1, column 1, negative d column 2, b row 2, column 1, c column 2, negative A
B
the fraction with numerator 1 and denominator absolute value of cap A the 2 by 2 matrix, row 1, column 1, d column 2, negative c row 2, column 1, negative b column 2, A
C
the fraction with numerator 1 and denominator absolute value of cap A the 2 by 2 matrix, row 1, column 1, A column 2, negative b row 2, column 1, negative c column 2, d
D
the fraction with numerator 1 and denominator absolute value of cap A the 2 by 2 matrix, row 1, column 1, d column 2, negative b row 2, column 1, negative c column 2, A
3

If C and D are matrices and C is the inverse of D , which of the following is true?

A
cap c cap d is equal to cap d cap c is equal to cap i
B
cap c plus cap d is equal to cap d plus cap c is equal to cap i
C
cap c minus cap d is equal to cap d minus cap c is equal to cap i
D
cap c over cap d is equal to cap d over cap c is equal to cap i
4

Which of the following matrices has an inverse?

A
the 1 by 3 row matrix column 1 4 column 2 negative 2 column 3 1
B
the 2 by 2 matrix, row 1, column 1, 6 column 2, negative 9 row 2, column 1, 2 column 2, 1
C
the 2 by 1 column matrix row 1 negative 6 row 2 3
D
the 2 by 3 matrix, row 1, column 1, negative 3 column 2, 5 column 3, 1 row 2, column 1, 4 column 2, negative 6 column 3, 0
5

Which expression represents the inverse of the matrix? the 2 by 2 matrix, row 1, column 1, 1 column 2, 3 row 2, column 1, negative 1 column 2, 2

A
1 fifth the 2 by 2 matrix, row 1, column 1, 2 column 2, negative 3 row 2, column 1, 1 column 2, 1
B
1 over negative 1 the 2 by 2 matrix, row 1, column 1, 2 column 2, negative 3 row 2, column 1, 1 column 2, 1
C
1 fifth the 2 by 2 matrix, row 1, column 1, negative 2 column 2, negative 3 row 2, column 1, 1 column 2, negative 1
D
1 over negative 1 the 2 by 2 matrix, row 1, column 1, negative 2 column 2, negative 3 row 2, column 1, 1 column 2, negative 1
8

Which pair of matrices are inverses of each other?

A
the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 3 halves row 2, column 1, 3 column 2, negative 4
B
the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 3 halves row 2, column 1, negative 3 column 2, 1
C
the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, 1 column 2, negative 3 halves row 2, column 1, negative 3 column 2, 4
D
the 2 by 2 matrix row 1, 2 3 row 2, 6 8 the 2 by 2 matrix, row 1, column 1, negative 4 column 2, 3 halves row 2, column 1, 3 column 2, negative 1
10

Which statement is true about the determinant of a matrix?

A
The determinant of an inverse matrix is equal to zero.
B
The determinant of an identity matrix is equal to zero.
C
The determinant of a zero matrix is equal to one.
D
The determinant of a singular matrix is equal to zero.

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