91Ó°ÊÓ

Evaluate the expression. $$ \left[\begin{array}{rr} 6 & 8 \\ -1 & 0 \end{array}\right]+\left[\begin{array}{rr} 0 & 5 \\ -3 & -1 \end{array}\right]+\left[\begin{array}{rr} -11 & -7 \\ 2 & -1 \end{array}\right] $$

Find the determinant of the matrix. $$ \left[\begin{array}{ll} -\frac{1}{2} & \frac{1}{3} \\ -6 & \frac{1}{3} \end{array}\right] $$

Evaluate the expression. $$ 4\left(\left[\begin{array}{rrr} -4 & 0 & 1 \\ 0 & 2 & 3 \end{array}\right]-\left[\begin{array}{rrr} 2 & 1 & -2 \\ 3 & -6 & 0 \end{array}\right]\right) $$

Identify the elementary row operation(s) being performed to obtain the new row-equivalent matrix. \(\begin{array}{ll}\text { Original Matrix } & \text { New Row-Equivalent Matrix }\end{array}\) $$ \left[\begin{array}{rrr} -2 & 5 & 1 \\ 3 & -1 & -8 \end{array}\right] \quad\left[\begin{array}{rrr} 13 & 0 & -39 \\ 3 & -1 & -8 \end{array}\right] $$

Find the inverse of the matrix (if it exists). $$ \left[\begin{array}{rr} 11 & 1 \\ -1 & 0 \end{array}\right] $$

Find the determinant of the matrix. $$ \left[\begin{array}{rr} \frac{2}{3} & \frac{4}{3} \\ -1 & -\frac{1}{3} \end{array}\right] $$

Find the inverse of the matrix (if it exists). $$ \left[\begin{array}{rr} -7 & 33 \\ 4 & -19 \end{array}\right] $$

Identify the elementary row operation(s) being performed to obtain the new row-equivalent matrix. \(\begin{array}{ll}\text { Original Matrix } & \text { New Row-Equivalent Matrix }\end{array}\) $$ \left[\begin{array}{rrr} 3 & -1 & -4 \\ -4 & 3 & 7 \end{array}\right] \quad\left[\begin{array}{rrr} 3 & -1 & -4 \\ 5 & 0 & -5 \end{array}\right] $$

Evaluate the expression. $$ -3\left(\left[\begin{array}{rr} 0 & -3 \\ 7 & 2 \end{array}\right]+\left[\begin{array}{rr} -6 & 3 \\ 8 & 1 \end{array}\right]\right)-2\left[\begin{array}{ll} 4 & -4 \\ 7 & -9 \end{array}\right] $$

Use the matrix capabilities of a graphing utility to find the determinant of the matrix. $$ \left[\begin{array}{rrr} 0.1 & 0.3 & 0.2 \\ -0.3 & -0.2 & 0.1 \\ 1 & 2 & 3 \end{array}\right] $$