Inverse, and Determinant

Which of the following best describes an identity matrix?

• A matrix with all elements equal to zero

• A square matrix with 1’s on the main diagonal and 0’s elsewhere

• A matrix with equal rows and columns

• A triangular matrix

Tags

CCSS.HSN.VM.C.10

What is the determinant of the identity matrix of order 3?

• 0

• 1

• 3

• –1

If A is an identity matrix, what is A×B for any matrix B of compatible size?

• Zero matrix

• Matrix B

• Identity matrix

• Undefined

Tags

CCSS.HSN.VM.C.10

Which condition must be satisfied for a square matrix A to have an inverse?

• det(A)=0

• det(A)≠0

• A must be triangular

• A must be symmetric

Tags

CCSS.HSA.REI.C.9

The inverse of a 2×2 matrix [a b c d] is:

• 1/(ad-bc) [d -b -c a]

• 1/(ab-cd) [d -c -b a]

• 1/(ad-bc) [-d b c -a]

• 1/(ad-bc) [a b c d]

Tags

CCSS.HSA.REI.C.9

What is the determinant of the matrix [4 2 1 3]?

• 10

• 12

• 8

• 5

If the determinant of a matrix is 0, then the matrix is said to be:

• Invertible

• Singular

• Identity

• Symmetric

For a 3×3 identity matrix I, what is I^2?

• Zero matrix

• Matrix with 2’s on the diagonal

• Identity matrix

• Undefined

Tags

CCSS.HSN.VM.C.10

Which of the following is true about determinants?

• The determinant of a triangular matrix is the product of its diagonal elements.

• The determinant of an identity matrix is always 0.

• Determinant only exists for 2×2 matrices.

• The determinant of a zero matrix is always 1.

If A×A^−1=I, then A^−1 is called:

• Cofactor matrix

• Adjoint matrix

• Inverse matrix

• Determinant

Tags

CCSS.HSA.REI.C.9