Matrices and Their Inverses / Assignment

Given: CD = I, and Find the elements of D. a = b = c = d = e = f = g = h = i =

-9, 7, 12, -5, 4, 7, 3, -2, -4

Determine if these matrices are inverses by calculating AB: c11 = c12 = c21 = c22 = So the matrices _________ inverses of one another. Now calculate BA: Find d11 = d12 = d21 = d22 = Based on these results, you can conjecture that mulitplying a matrix by its inverse _______.

1, 0, 0, 1 / are / 1, 0, 0, 1 / is commutative

Which pairs of matrices are inverses?

B

Select the matrix that is the inverse of:

C

Internet sites often ask for a secret phrase to recover lost passwords. Jason encoded a secret phrase using matrix multiplication. He multiplied the clear text code for each letter by the matrix:The matrix representing the encoded text is:Jason's secret phrase is:

CATS RULE DOGS DROOL

Explain why it is important to be able to perform matrix operations by hand when a calculator can do them for you.

Calculators may not always be available. Finding an inverse by hand allows me to understand the process. Calculators may not show the elements of a matrix as fractions. Sometimes it is faster by hand. A matrix could contain a variable.

Suppose matrix B is the inverse of matrix A. Use your knowledge of inverses and matrix multiplication to answer the following:

I, A, B, I

Which of the following statements are true about inverse matrices? All square matrices have inverses. If A and B are inverse matrices, then A and B must be square matrices. The determinant of a singular matrix is equal to zero. If A and B are inverse matrices, then A + B = I. If A and B are inverse matrices, then . Any zero matrix does not have an inverse. If B = A-1, then A = B-1.

If A and B are inverse matrices, then A and B must be square matrices. The determinant of a singular matrix is equal to zero. If A and B are inverse matrices, then . Any zero matrix does not have an inverse. If B = A-1, then A = B-1.