91Ó°ÊÓ

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

Describe the information necessary to make a matrix containing numerical data meaningful.

State the dimensions of each matrix. Identify the indicated element. \(\left[\begin{array}{lll}{1} & {1} & {1} \\ {1} & {0} & {0} \\ {1} & {0} & {0}\end{array}\right], a_{32}\)

Find the inverse of each matrix, if it exists. $$ \left[\begin{array}{rrr}{0} & {0} & {2} \\ {1} & {4} & {-2} \\ {3} & {-2} & {1}\end{array}\right] $$

Each matrix represents the vertices of a polygon. Translate each figure 5 units left and 1 unit up. Express your answer as a matrix. $$ \left[\begin{array}{cccc}{-3} & {0} & {3} & {0} \\ {-9} & {-6} & {-9} & {-12}\end{array}\right] $$

Determine whether the matrices are multiplicative inverses. If they are not, explain why not. $$ \left[\begin{array}{cc}{2} & {0.5} \\ {5} & {1}\end{array}\right],\left[\begin{array}{cc}{-2} & {1} \\ {10} & {-4}\end{array}\right] $$

Find the sum of \(E=\left[\begin{array}{l}{3} \\ {4} \\\ {7}\end{array}\right]\) and the additive inverse of \(G=\left[\begin{array}{r}{-2} \\ {0} \\ {5}\end{array}\right]\)

Prove that matrix addition is commutative for \(2 \times 2\) matrices.

Multiple choice Suppose you invested \(\$ 5000\) in three different funds for one year. The funds paid simple interest of \(8 \%, 10 \%\) , and 7\(\%\) , respectively. The total interest at the end of one year was \(\$ 405 .\) You invested \(\$ 500\) more at 10\(\%\) than at 8\(\%\) . How much did you invest in the 10\(\%\) fund? \(\begin{array}{ll}{\text { A } \$ 150} & {\text { B } \$ 1000}\end{array}\) C \(\$ 1500 \quad\) D \(\$ 2500\)

Determine whether each matrix has an inverse. If an inverse matrix exists, find it. $$ \left[\begin{array}{rr}{-3} & {4} \\ {9} & {10}\end{array}\right] $$