7. Systems of Equations & Matrices

In Exercises 13 - 18, use the fact that ifa b d - bA = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c aeach matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 2 3A = - 1 2

In Exercises 43–44, (a) Write each linear system as a matrix equation in the form AX = B (b) Solve the system using the inverse that is given for the coefficient matrix.

In Exercises 39–42, find A^(-1) Check that AA^-1 = I and A^(-1)A = I

In Exercises 37–38, find the products and to determine whether B is the multiplicative inverse of A.

Answer each question. What is the product of [2x2 matrix] and I2 (in either order)?

Answer each question. What is the product [3x3 matrix] [3x3 matrix]?

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I￬n.) [2x2 matrix] and [2x2 matrix]

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I￬n.) [3x3 matrix] and [3x3 matrix]

Find the inverse, if it exists, for each matrix. [2x2 matrix]

Find the inverse, if it exists, for each matrix. [2x2 matrix]

Find the inverse, if it exists, for each matrix. [2x2 matrix]

Find the inverse, if it exists, for each matrix. [3x3 matrix]

Find the inverse, if it exists, for each matrix. [3x3 matrix]

Find the inverse, if it exists, for each matrix. [3x3 matrix]