91Ó°ÊÓ

Concept Check The product \(M N\) of two matrices can be found only if the number of number of____ \(M\) equals the number of ________ of \(N.\)

Use a graphing calculator to solve each system. Express solutions with approximations to the nearest thousandth. $$\begin{aligned}&\sqrt{5} x+\sqrt[3]{6} y=9\\\&\sqrt{2} x+\sqrt[5]{9} y=12\end{aligned}$$

Graph the solution set of each system of inequalities by hand. $$\begin{array}{r} x+y \leq 36 \\ -4 \leq x \leq 4 \end{array}$$

Use row operations on an augmented matrix to solve each system of equations. Round to nearest thousandth when appropriate. $$\begin{aligned} 2 x-y+3 z &=0 \\ x+2 y-z &=5 \\ 2 y+z &=1 \end{aligned}$$

Concept Check In finding the product \(A B\) of matrices \(A\) and \(B,\) the first row, second column, entry is found by multiplying the ______ elements in \(A\) and the ______ elements in \(B\) and then ______ these products.

A total of \(\$ 5000\) is invested at \(2 \%, 3 \%,\) and 4\%. The amount invested at \(4 \%\) equals the total amount invested at \(2 \%\) and \(3 \% .\) The total interest for one year is \(\$ 145 .\) If possible, find the amount invested at each interest rate. Interpret your answer.

Graph the solution set of each system of inequalities by hand. $$\begin{aligned} &y > x^{2}+4 x+4\\\ &y < -x^{2} \end{aligned}$$

Solve each system by using the matrix inverse method. $$\begin{array}{l} 2.1 x+y=\sqrt{5} \\ \sqrt{2} x-2 y=5 \end{array}$$

Use a graphing calculator to solve each system. Express solutions with approximations to the nearest thousandth. $$\begin{aligned}&\pi x+e y=3\\\&e x+\pi y=4\end{aligned}$$

Use row operations on an augmented matrix to solve each system of equations. Round to nearest thousandth when appropriate. $$\begin{aligned} 4 x+2 y-3 z &=6 \\ x-4 y+z &=-4 \\ -x+2 z &=2 \end{aligned}$$