91Ó°ÊÓ

Determine whether the matrices \(A\) and \(B\) are equal. $$ A=\left[\begin{array}{cc}{\frac{1}{4}} & {\ln 1} \\ {2} & {3}\end{array}\right], \quad B=\left[\begin{array}{cc}{0.25} & {0} \\\ {\sqrt{4}} & {\frac{6}{2}}\end{array}\right] $$

1–14 Graph the inequality. $$y \geq-2$$

Use the substitution method to find all solutions of the system of equations. \(\left\\{\begin{array}{c}{2 x+y=7} \\ {x+2 y=2}\end{array}\right.\)

\(1-8\) Find the determinant of the matrix, if it exists. $$ \left[\begin{array}{rr}{0} & {-1} \\ {2} & {0}\end{array}\right] $$

State whether the equation or system of equations is linear. $$ x^{2}+y^{2}+z^{2}=4 $$

Graph each linear system, either by hand or using a graphing device. Use the graph to determine if the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it. $$\left\\{\begin{array}{c}{2 x+y=11} \\ {x-2 y=4}\end{array}\right.$$

1–6 State the dimension of the matrix. $$\left[\begin{array}{rrrr}{-1} & {5} & {4} & {0} \\ {0} & {2} & {11} & {3}\end{array}\right]$$

Calculate the products \(A B\) and \(B A\) to verify that \(B\) is the inverse of \(A .\) \(A=\left[\begin{array}{ll}{2} & {-3} \\ {4} & {-7}\end{array}\right], \quad B=\left[\begin{array}{ll}{\frac{7}{2}} & {-\frac{3}{2}} \\ {2} & {-1}\end{array}\right]\)

Use the substitution method to find all solutions of the system of equations. \(\left\\{\begin{array}{l}{y=x^{2}} \\ {y=x+12}\end{array}\right.\)

Perform the matrix operation, or if it is impossible, explain why. $$ \left[\begin{array}{rr}{2} & {6} \\ {-5} & {3}\end{array}\right]+\left[\begin{array}{rr}{-1} & {-3} \\ {6} & {2}\end{array}\right] $$