91Ó°ÊÓ

Show that the matrices are multiplicative inverses. $$ \left[\begin{array}{rr}{3} & {2} \\ {4} & {3}\end{array}\right],\left[\begin{array}{rr}{3} & {-2} \\ {-4} & {3}\end{array}\right] $$

State the dimensions of each matrix. \(\left[\begin{array}{rrr}{4} & {-2} & {2} \\ {1} & {4} & {1} \\ {0} & {5} & {-7}\end{array}\right]\)

Use matrix addition to find the coordinates of each image after a translation of 3 units left and 5 units up. If possible, graph each pair of figures on the same coordinate plane. $$A(1,-3), B(1,1), C(5,1), D(5,-3)$$

Use matrices \(A, B, C,\) and \(D .\) Find each product, sum, or difference. $$A=\left[\begin{array}{rr}{3} & {4} \\ {6} & {-2} \\ {1} & {0}\end{array}\right] \quad B=\left[\begin{array}{rr}{-3} & {1} \\ {2} & {-4} \\\ {-1} & {5}\end{array}\right] \quad C=\left[\begin{array}{rr}{1} & {2} \\\ {-3} & {1}\end{array}\right] \quad D=\left[\begin{array}{ll}{5} & {1} \\ {0} & {2}\end{array}\right]$$ $$ 3 A $$

Evaluate the determinant of each matrix. $$ \left[\begin{array}{lll}{1} & {2} & {5} \\ {3} & {1} & {0} \\ {1} & {2} & {1}\end{array}\right] $$

Use Cramer's Rule to solve each system. $$ \left\\{\begin{array}{l}{2 x+y=4} \\ {3 x-y=6}\end{array}\right. $$

Write each system as a matrix equation. Identify the coefficient matrix, the variable matrix, and the constant matrix. $$ \left\\{\begin{array}{l}{x+y=5} \\ {x-2 y=-4}\end{array}\right. $$

Find each sum or difference. $$ \left[\begin{array}{rrr}{2} & {-3} & {4} \\ {5} & {6} & {-7}\end{array}\right]+\left[\begin{array}{ccc}{0} & {0} & {0} \\ {0} & {0} & {0}\end{array}\right] $$

Evaluate the determinant of each matrix. $$ \left[\begin{array}{lll}{1} & {4} & {0} \\ {2} & {3} & {5} \\ {0} & {1} & {0}\end{array}\right] $$

Use matrix addition to find the coordinates of each image after a translation of 3 units left and 5 units up. If possible, graph each pair of figures on the same coordinate plane. $$ G(0,0), H(4,4), I(4,-4), J(8,0) $$