91Ó°ÊÓ

Verify that each system of equations has the indicated solution. \(\left\\{\begin{aligned} x+5 y &=-6 \\\\-x+2 y &=-8 \end{aligned}\right.\) Solution: \(x=4, y=-2\)

Evaluate the determinant of \(A\). $$A=\left[\begin{array}{rr} 5 & -\frac{2}{5} \\ 10 & 2 \end{array}\right]$$

Construct the augmented matrix for each system of equations. Do not solve the system. $$\left\\{\begin{array}{l}-2 x+6 z=-1 \\\\-3 x+2 y+z=0\end{array}\right.$$

In Exercises \(1-34\), find all real solutions of the system of equations. If no real solution exists, so state. $$\left\\{\begin{array}{c} x^{2}+y=4 \\ 2 x+y=1 \end{array}\right.$$

Verify that each system of equations has the indicated solution. \(\left\\{\begin{array}{r}-x-2 y=5 \\ -2 x+y=-5\end{array}\right.\) Solution: \(x=1, y=-3\)

Write just the form of the partial fraction decomposition. Do not solve for the constants. $$\frac{2 x^{2}-5}{x^{4}-1}$$

Indicate whether each statement is True or False. Explain your answers. Some matrices that do not have the same dimensions can be multiplied.

Use back-substitution to solve the system of linear equations. $$\left\\{\begin{aligned} x+y-z &=-1 \\ -y-3 z &=-2 \\ 2 z &=4 \end{aligned}\right.$$

In Exercises \(1-34\), find all real solutions of the system of equations. If no real solution exists, so state. $$\left\\{\begin{array}{r} 3 x^{2}-10 y=5 \\ x-y=-2 \end{array}\right.$$

Write just the form of the partial fraction decomposition. Do not solve for the constants. $$\frac{x+6}{3 x^{3}+6 x^{2}+3 x}$$