91Ó°ÊÓ

Exer. 3-12: Find the inverse of the matrix if it exists. $$ \left[\begin{array}{rr} 2 & -4 \\ 1 & 3 \end{array}\right] $$

Find, if possible, \(A+B, A-B, 2 A\), and \(-3 B\) $$ A=\left[\begin{array}{rrr} 0 & -2 & 7 \\ 5 & 4 & -3 \end{array}\right], \quad B=\left[\begin{array}{lll} 8 & 4 & 0 \\ 0 & 1 & 4 \end{array}\right] $$

\(\left\\{\begin{aligned} 4 x-y+3 z &=6 \\\\-8 x+3 y-5 z &=-6 \\ 5 x-4 y &=-9 \end{aligned}\right.\)

Exer. 3-4: Sketch the region \(R\) determined by the given constraints, and label its vertices. Find the maximum value of \(C\) on \(R\). $$ \begin{aligned} &C=4 x-2 y \\ &x-2 y \geq-8, \quad 7 x-2 y \leq 28, \quad x+y \geq 4 \end{aligned} $$

1-30: Use the method of substitution to solve the system. $$ \left\\{\begin{array}{r} y^{2}=x \\ x+2 y+3=0 \end{array}\right. $$

Exer. 1-28: Find the partial fraction decomposition. $$ \frac{5 x-12}{x^{2}-4 x} $$

Exer. 1-14: Without expanding, explain why the statement is true. $$ \left|\begin{array}{lll} 1 & 1 & 2 \\ 1 & 0 & 1 \\ 2 & 1 & 1 \end{array}\right|=\left|\begin{array}{lll} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 2 & 1 & 1 \end{array}\right| $$

Solve the system. $$ \left\\{\begin{array}{l} 7 x-8 y=9 \\ 4 x+3 y=-10 \end{array}\right. $$

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

Find, if possible, \(A+B, A-B, 2 A\), and \(-3 B\) $$ A=\left[\begin{array}{lll} 4 & -3 & 2 \end{array}\right], \quad B=\left[\begin{array}{lll} 7 & 0 & -5 \end{array}\right] $$