91Ó°ÊÓ

Find the inverse of the matrix (if it exists). $$\left[\begin{array}{rrr}3 & 2 & 5 \\\2 & 2 & 4 \\\\-4 & 4 & 0\end{array}\right]$$

Determine whether the stochastic matrix \(P\) is regular. Then find the steady state matrix \(X\) of the Markov chain with matrix of transition probabilities \(P\). $$P=\left[\begin{array}{ll} 0 & 0.3 \\ 1 & 0.7 \end{array}\right]$$

Perform the operations, given \(c=-2\) and \(A=\left[\begin{array}{rrr}1 & 2 & 3 \\\ 0 & 1 & -1\end{array}\right], B=\left[\begin{array}{rr}1 & 3 \\ -1 & 2\end{array}\right], C=\left[\begin{array}{rr}0 & 1 \\ -1 & 0\end{array}\right]\). $$(B+C) A$$.

Find the least squares regression line. $$ (0,0),(1,1),(2,4) $$

Find the inverse of the matrix (if it exists). $$\left[\begin{array}{lll}2 & 0 & 0 \\\0 & 3 & 0 \\\0 & 0 & 5\end{array}\right]$$

Determine whether the stochastic matrix \(P\) is regular. Then find the steady state matrix \(X\) of the Markov chain with matrix of transition probabilities \(P\). $$P=\left[\begin{array}{ll} 1 & 0.75 \\ 0 & 0.25 \end{array}\right]$$

Find the inverse of the elementary matrix. $$ \left[\begin{array}{ll} 5 & 0 \\ 0 & 1 \end{array}\right] $$

Find the least squares regression line. $$ (1,0),(3,3),(5,6) $$

Find, if possible, (a) \(A B\) and (b) \(B A\) $$A=\left[\begin{array}{rrr} 3 & 2 & 1 \\ -3 & 0 & 4 \\ 4 & -2 & -4 \end{array}\right], \quad B=\left[\begin{array}{rr} 1 & 2 \\ 2 & -1 \\ 1 & -2 \end{array}\right]$$

Determine whether the stochastic matrix \(P\) is regular. Then find the steady state matrix \(X\) of the Markov chain with matrix of transition probabilities \(P\). $$P=\left[\begin{array}{ll} 0.2 & 0 \\ 0.8 & 1 \end{array}\right]$$