91Ó°ÊÓ

Show that \(B\) is the inverse of \(A\) $$A=\left[\begin{array}{ll}1 & 2 \\\3 & 4\end{array}\right], \quad B=\left[\begin{array}{rr}-2 & 1 \\\\\frac{3}{2} & -\frac{1}{2}\end{array}\right]$$

Find \(x\) and \(y\) $$\left[\begin{array}{rrrr} 16 & 4 & 5 & 4 \\ -3 & 13 & 15 & 6 \\ 0 & 2 & 4 & 0 \end{array}\right]=\left[\begin{array}{rrrr} 16 & 4 & 2 x+1 & 4 \\ -3 & 13 & 15 & 3 x \\ 0 & 2 & 3 y-5 & 0 \end{array}\right]$$

Determine whether the matrix is stochastic. $$\left[\begin{array}{lll} 0 . \overline{3} & 0.1 \overline{6} & 0.25 \\ 0 . \overline{3} & 0 . \overline{6} & 0.25 \\ 0 . \overline{3} & 0.1 \overline{6} & 0.5 \end{array}\right]$$

Show that \(B\) is the inverse of \(A\) $$A=\left[\begin{array}{rr}1 & -1 \\\2 & 3\end{array}\right], \quad B=\left[\begin{array}{rr}\frac{3}{5} & \frac{1}{5} \\\\-\frac{2}{5} & \frac{1}{5}\end{array}\right]$$

Determine whether the matrix is stochastic. $$\left[\begin{array}{lll} 0.3 & 0.5 & 0.2 \\ 0.1 & 0.2 & 0.7 \\ 0.8 & 0.1 & 0.1 \end{array}\right]$$

Find \(x\) and \(y\) $$\left[\begin{array}{rrr} x+2 & 8 & -3 \\ 1 & 2 y & 2 x \\ 7 & -2 & y+2 \end{array}\right]=\left[\begin{array}{rrr} 2 x+6 & 8 & -3 \\ 1 & 18 & -8 \\ 7 & -2 & 11 \end{array}\right]$$

Find, if possible, (a) \(\boldsymbol{A}+\boldsymbol{B},\) (b) \(\boldsymbol{A}-\boldsymbol{B},\) (c) \(\boldsymbol{2} \boldsymbol{A},\) (d) \(\boldsymbol{2} \boldsymbol{A}-\boldsymbol{B},\) and (e) \(B+\frac{1}{2} A\) $$A=\left[\begin{array}{ll} 1 & 2 \\ 2 & 1 \end{array}\right], \quad B=\left[\begin{array}{rr} -3 & -2 \\ 4 & 2 \end{array}\right]$$

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

Determine whether the matrix is stochastic. $$\left[\begin{array}{llll} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$$

Show that \(B\) is the inverse of \(A\) $$A=\left[\begin{array}{rrr}-2 & 2 & 3 \\\1 & -1 & 0 \\\0 & 1 & 4 \end{array}\right], \quad B=\frac{1}{3}\left[\begin{array}{rrr}-4 & -5 & 3 \\\\-4 & -8 & 3 \\\1 & 2 & 0\end{array}\right]$$