Systems of Equations and Inequalities

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

A+B

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$A-B$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

4$A$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$-3B$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$3A - 2B$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$2A+4B$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$AC$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$BC$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$CA$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

Use the following matrices to evaluate the given expression.

$$\begin{gathered} A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right] \\ C(A+B) \end{gathered}$$

Use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right], C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$(A+B)C$

In Problems 9–24, use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right]; B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right]; C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$AC-3I_2$

In Problems 9–24, use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right]; B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right]; C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$CA+5I_3$

In Problems 9–24, use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right]; B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right]; C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$CA-CB$

In Problems 9–24, use the following matrices to evaluate the given expression.

$A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right]; B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right]; C=\left[\begin{array}{cc}4& 1\\ 6& 2\\ -2& 3\end{array}\right]$

$AC+BC$

In Problems 25– 30, find the product.

$\left[\begin{array}{cc}2& -2\\ 1& 0\end{array}\right]\left[\begin{array}{cccc}2& 1& 4& 6\\ 3& -1& 3& 2\end{array}\right]$

In Problems 25– 30, find the product.

In Problems 25– 30, find the product.

$\left[\begin{array}{ccc}1& 2& 3\\ 0& -1& 4\end{array}\right]\left[\begin{array}{cc}1& 2\\ -1& 0\\ 2& 4\end{array}\right]$

In Problems 25– 30, find the product.

$\left[\begin{array}{cc}1& -1\\ -3& 2\\ 0& 5\end{array}\right]\left[\begin{array}{ccc}2& 8& -1\\ 3& 6& 0\end{array}\right]$

In Problems 25– 30, find the product.

$\left[\begin{array}{ccc}1& 0& 1\\ 2& 4& 1\\ 3& 6& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 6& 2\\ 8& -1\end{array}\right]$

In Problems 25– 30, find the product.

$\left[\begin{array}{ccc}4& -2& 3\\ 0& 1& 2\\ -1& 0& 1\end{array}\right]\left[\begin{array}{cc}2& 6\\ 1& -1\\ 0& 2\end{array}\right]$

In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.

$\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]$

In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.
$\left[\begin{array}{cc}3& -1\\ -2& 1\end{array}\right]$

In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.
$\left[\begin{array}{cc}6& 5\\ 2& 2\end{array}\right]$

In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.
$\left[\begin{array}{cc}-4& 1\\ 6& -2\end{array}\right]$

In Problems 31– 40, each matrix is non singular. Find the inverse of each matrix.
$\left[\begin{array}{cc}2& 1\\ a& a\end{array}\right]$

In Problems $31-40$, each matrix is nonsingular. Find the inverse of each matrix.

$\left[\begin{array}{ll}b& 3\\ b& 2\end{array}\right] b\ne 0$

In Problems $31-40$, each matrix is nonsingular. Find the inverse of each matrix.

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

In Problems $31-40$, each matrix is nonsingular. Find the inverse of each matrix.

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

In Problems $31-40$, each matrix is nonsingular. Find the inverse of each matrix.

$\left[\begin{array}{ccc}1& 1& 1\\ 3& 2& -1\\ 3& 1& 2\end{array}\right]$

In Problems $31-40$, each matrix is nonsingular. Find the inverse of each matrix.

$\left[\begin{array}{ccc}3& 3& 1\\ 1& 2& 1\\ 2& -1& 1\end{array}\right]$

In Problems $41-60$, use the inverses found in Problems 31–40 to solve each system of equations.

$\left\{\begin{array}{l}2x+y=8\\ x+y=5\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}3x-y=8\\ -2x+y=4\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}2x+y=0\\ x+y=5\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}3x-y=4\\ -2x+y=5\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}6x+5y=7\\ 2x+2y=2\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}-4x+y=0\\ 6x-2y=14\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}6x+5y=13\\ 2x+2y=5\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}-4x+y=5\\ 6x-2y=-9\end{array}\right.$

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}2x+y=-3\\ ax+ay=-a\end{array}\right. a\ne 0$.

In Problems $41-60$, use the inverses found in Problems $31-40$ to solve each system of equations.

$\left\{\begin{array}{l}bx+3y=2b+3\\ bx+2y=2b+2\end{array} b\ne 0\right.$

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations 

$\left\{\begin{array}{r}2x+y=\frac{7}{a}\\ ax+ay=5\end{array} a\ne 0\right.$

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations. 

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations. 

$\left\{\begin{array}{rr}x-y+z=& 0\\ -2y+z=& -1\\ -2x-3y=& -5\end{array}\right.$

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations

$\left\{\begin{array}{rr}x+2z=& 6\\ -x+2y+3z=& -5\\ x-y=& 6\end{array}\right.$

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equations

$\left\{\begin{array}{r}x-y+z=2\\ -2y+z=2\\ -2x-3y=\frac{1}{2}\end{array}\right.$

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equation 

$\left\{\begin{array}{rr}x+2z=& 2\\ -x+2y+3z=& -\frac{3}{2}\\ x-y=& 2\end{array}\right.$

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equation 

$\left\{\begin{array}{c}x+y+z=9\\ 3x+2y-z=8\\ 3x+y+2z=1\end{array}\right.$

In Problems 41– 60, use the inverses found in Problems 31–40 to solve each system of equation

$\left\{\begin{array}{r}3x+3y+z=8\\ x+2y+z=5\\ 2x-y+z=4\end{array}\right.$