7. Systems of Equations & Matrices

Use the fact that if , then to find the inverse of each matrix, if possible. Check that $A{A}^{-1}=I_2$ and $A^{-1}A=I_2$.

$A = \begin{bmatrix}3 & -1 \\-4 & 2\end{bmatrix}$

Use the fact that if , then to find the inverse of each matrix, if possible. Check that $A{A}^{-1}=I_2$ and $A^{-1}A=I_2$.

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 and I₂ (in either order)?

Answer each question. What is the product ?

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

Find the inverse, if it exists, for each matrix.

Find the inverse, if it exists, for each matrix.

Find the inverse, if it exists, for each matrix.

Find the inverse, if it exists, for each matrix.

Find the inverse, if it exists, for each matrix.

Find the inverse, if it exists, for each matrix.