### About Transpose of a Matrix:

Suppose we have matrix A, which is an m x n matrix. The transpose of A will be an n x m matrix whose columns are formed from the corresponding rows of our matrix A. For a square matrix, the concept is the same, however, the order will not change.

Test Objectives
• Demonstrate the ability to find the transpose of a matrix
Transpose of a Matrix Practice Test:

#1:

Instructions: find the transpose.

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cc}5 & 3\\ 4 & 7\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}1 & -3 & 7\\ -2 & 5 & 4\end{array}\right]$$

#2:

Instructions: find the transpose.

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cc}4 & -20 \\ -8 & 6 \\5 & -7\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}-6 & -1 & 2 \\ -7 & 3 & -1 \\ 13 & 1 & 5 \end{array}\right]$$

#3:

Instructions: find the transpose.

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}0 & 8 & -5\\ -15 & 2 & 11 \\-7 & 6 & 4\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{cccc}5 & 19 & 3 & -1\\ 2 & -4 & -3 & 2 \\-10 & 0 & 7 & -8\end{array}\right]$$

#4:

Instructions: find the transpose.

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cccc}-11 & 31 & 1 & -5\\ 6 & -2 & 3 & -1 \\1 & 0 & 5 & -2 \\ 1 & -4 & 8 & 7\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{ccccc}1 & 5 & -2 & -3 & 0\\ 9 & 8 & 6 & 5 & 3 \\11 & -1 & 0 & 0 & 2 \\ -4 & 2 & 3 & 14 & 8\end{array}\right]$$

#5:

Instructions: find the transpose.

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cccc}0 & 4 & 3 & -1\\ -4 & 7 & -7 & 2 \\0 & 1 & 9 & -3\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{cccc}5 & -11 & 3 & -1\\ 10 & -2 & 14 & 3 \end{array}\right]$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cc}5 & 4\\ 3 & 7\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{cc}1 & -2\\ -3 & 5\\7 & 4\end{array}\right]$$

#2:

Solutions:

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}4 & -8 & 5\\ -20 & 6 & -7\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}-6 & -7 & 13\\ -1 & 3 & 1 \\2 & -1 & 5\end{array}\right]$$

#3:

Solutions:

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}0 & -15 & -7\\ 8 & 2 & 6 \\-5 & 11 & 4\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}5 & 2 & -10\\ 19 & -4 & 0 \\3 & -3 & 7 \\-1 & 2 & -8\end{array}\right]$$

#4:

Solutions:

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cccc}-11 & 6 & 1 & 1\\ 31 & -2 & 0 & -4 \\1 & 3 & 5 & 8 \\-5 & -1 & -2 & 7\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{cccc}1 & 9 & 11 & -4\\ 5 & 8 & -1 & 2 \\-2 & 6 & 0 & 3 \\-3 & 5 & 0 & 14 \\0 & 3 & 2 & 8\end{array}\right]$$

#5:

Solutions:

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}0 & -4 & 0\\ 4 & 7 & 1 \\3 & -7 & 9 \\-1 & 2 & -3\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{cc}5 & 10 \\ -11 & -2 \\3 & 14 \\-1 & 3 \end{array}\right]$$