# Chapter 4: Matrices

Q1.

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.

For any matrix${A}_{m\times n}$for$m\ne n$, ${A}^{2}$is defined.

Q1.

Solve each equation. 1$\left[\begin{array}{c}3\text{x}+1\\ 7\text{y}\end{array}\right]=\left[\begin{array}{c}19\\ 21\end{array}\right]$

Q1.

Write the $\mathbf{4}\mathbf{\times}\mathbf{4}$ identity matrix.

Q1.

Describe the conditions under which matrices can be added or subtracted.

Q1.

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.

- Write the coordinates in a vertex matrix.

Q1.

Describe the condition that must be met in order to use Cramer’s rule.

Q1.

Compare and contrast the size and shape of the pre-image and image for each type of transformation. Tell which transformations are isometries.

Q1.

Write a matrix whose determinant is zero.

Q1.

Describe the conditions that must be met in order for two matrices to be considered equal.

Q10.

For exercises 7-10, use the rectangle at the right

10. Find the coordinates of the image after a rotation of $180\xb0$