91Ó°ÊÓ

$$ \left[\begin{array}{ll} 1 & 1 \\ 6 & 6 \end{array}\right] $$

Compute the products. Some of these may be undefined.Exercises marked I should be done using technology. The others should be done two ways: by hand and by using technology where possible. \(\left[\begin{array}{lll}0 & 1 & -1 \\ 3 & 1 & -1\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 4 & 2 \\ 0 & 1\end{array}\right]\)

$$ \left[\begin{array}{lll} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array}\right] $$

Compute the products. Some of these may be undefined.Exercises marked I should be done using technology. The others should be done two ways: by hand and by using technology where possible. \(\left[\begin{array}{rr}1 & 0 \\ 1 & -1\end{array}\right]\left[\begin{array}{ll}0 & 1 \\ 0 & 1\end{array}\right]\)

Evaluate the given expression. Take$$\begin{aligned}&A=\left[\begin{array}{rr}0 & -1 \\\1 & 0 \\\\-1 & 2 \end{array}\right], B=\left[\begin{array}{rr}0.25 & -1 \\\0 & 0.5 \\\\-1 & 3\end{array}\right], \text { and } \\\&C=\left[\begin{array}{rr}1 & -1 \\\1 & 1 \\\\-1 & -1\end{array}\right].\end{aligned}$$ $$ A+B-C $$

Decide whether the game is strictly determined. If it is, give the players'optimal pure strategies and the value of the game. $$ \begin{gathered} \text { B } \\ p & q \\ \text { A } \left.\begin{array}{rr} a \\ 1 & 1 \\ 2 & -4 \end{array}\right] \end{gathered} $$

Let \((I-A)^{-1}=\left[\begin{array}{lll}1.5 & 0.1 & 0 \\ 0.2 & 1.2 & 0.1 \\\ 0.1 & 0.7 & 1.6\end{array}\right]\) and assume that the external demand for the products in Sector 1 increases by I unit. By how many units should each sector increase production? What do the columns of the matrix \((I-A)^{-1}\) tell you? HIIIT [See Quick Example on page 230.]

Let \((I-A)^{-1}=\left[\begin{array}{lll}1.5 & 0.1 & 0 \\ 0.1 & 1.1 & 0.1 \\\ 0 & 0 & 1.3\end{array}\right]\), and assume that the external demand for the products in each of the sectors increases by 1 unit. By how many units should each sector increase production?

$$ \left[\begin{array}{lll} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{array}\right] $$

Decide whether the game is strictly determined. If it is, give the players'optimal pure strategies and the value of the game. $$ \begin{array}{rr} & \mathbf{B} \\ p & q \\ \mathbf{A}_{b} & a \\ b & {\left[\begin{array}{rr} -1 & 2 \\ 10 & -1 \end{array}\right]} \end{array} $$