91Ó°ÊÓ

Use $A=\left[\begin{array}{cc}1& −2\\ 4& 3\end{array}\right]$,$B=\left[\begin{array}{cc}-5& 2\\ 4& 3\\ & \end{array}\right]$, and$C=\left[\begin{array}{cc}5& 1\\ 2& -4\\ & \end{array}\right]$and scalar $c=3$to determine whether the equation is true for the given matrices.

$C\left(A+B\right)=AC+BC$

Write a translation matrix that moves $\mathrm{Δ}DEF$up and left on the coordinate plane.

What is meant by corresponding elements.

Create a square matrix that does not have an inverse.

For Exercises 1-3, reflect square $\mathbf{ABCD}$ with vertices $\mathbf{A}\left(\mathbf{1}\mathbf{,}\mathbf{2}\right)$, $\mathbf{B}\left(\mathbf{4}\mathbf{,}\mathbf{-}\mathbf{1}\right)$, $\mathbf{C}\left(\mathbf{1}\mathbf{,}\mathbf{-}\mathbf{4}\right)$ and $\mathbf{D}\left(\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{-}\mathbf{1}\right)$ over the y-axis.

3. Graph $\mathbf{ABCD}$ and $\mathbf{A}\mathbf{\text{'}}\mathbf{B}\mathbf{\text{'}}\mathbf{C}\mathbf{\text{'}}\mathbf{D}\mathbf{\text{'}}$.

Solve each equation.3$\left[\begin{array}{cc}2& \text{x}\\ \text{y}& 5\end{array}\right]=\left[\begin{array}{cc}2& 1\\ 3& \text{z}\end{array}\right]$

Explain why, in most cases$(A+B)C≠CA+CB$

Write a system of equations whose solution is

$x=\frac{\left|\begin{array}{cc}−6& 5\\ 30& −2\end{array}\right|}{\left|\begin{array}{cc}3& 5\\ 4& −2\end{array}\right|}$$y=\frac{\left|\begin{array}{cc}3& −6\\ 4& 30\end{array}\right|}{\left|\begin{array}{cc}3& 5\\ 4& −2\end{array}\right|}$

Explain why$\left[\begin{array}{ccc}2& 1& 7\\ 3& −5& 0\end{array}\right]$doesn’t have a determinant.

Write a matrix that, when added to a $3×2$matrix, increases each element in the matrix by 4.