A matrix is an ordered array of numbers. The order of a matrix is stated as the number of rows by the number of columns. For example, a matrix with 3 rows and 4 columns has an order of 3 x 4. If we have a matrix A, then a1,3 would be the element in A that is in the first row and third column. Two matrices are equal if and only if they have the same order or size and each corresponding element is equal.

Test Objectives
• Demonstrate the ability to find the order of a matrix
• Demonstrate the ability to find a specific entry in a matrix
• Demonstrate the ability to solve a matrix equation
Introduction to Matrices Practice Test:

#1:

Instructions: state the order.

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

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}-9 & 19 & 17\\ 2 & 3 & 0 \\ 1 & -1 & 5\end{array}\right]$$

#2:

Instructions: state the order.

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{ccccc}5 & 2 & 19 & 13 & 22 \\ -17 & -4 & 8 & 29 & 1 \\ -9 & -7 & -3 & 44 & 50\end{array}\right]$$

Instructions: what is element: a1,2

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

#3:

Instructions: what is element: a2,3

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}5 & 6 \\ 1 & -1 \\ 7 & 3\end{array}\right]$$

b) What type of matrix has the same number of rows as columns?

#4:

Instructions: if A = B, what is the value of x?

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}1 & 5 \\ 6 & x\end{array}\right]$$ $$B=\left[ \begin{array}{cc}1 & 5 \\ 6 & 7\end{array}\right]$$

Instructions: if A = B, what is the value of x and y?

$$b)\hspace{.2em}$$

$$A=\left[ \begin{array}{cc}-3 & 1 \\ 6 & x + 5\end{array}\right]$$ $$B=\left[ \begin{array}{cc}y + 2 & 1 \\ 6 & -2\end{array}\right]$$

#5:

Instructions: find x, y, and z such that A = B.

$$a)\hspace{.2em}$$

$$A=\left[ \begin{array}{ccc}-1 & 5 & 9 \\ x - 1 & y + 2 & 4\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}-1 & 5 & 9 \\ 13 & -21 & z + 4\end{array}\right]$$

$$b)\hspace{.2em}$$

$$A=\left[ \begin{array}{ccc}3 & 5 & 11 \\ x + 1 & y - 7 & 7\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}3 & 11 & 5 \\ -14 & 12 & z - 9\end{array}\right]$$
Written Solutions:

#1:

Solutions:

a) 2 x 3

b) 3 x 3

#2:

Solutions:

a) 3 x 5

b) 6

#3:

Solutions:

a) Doesn't exist

b) Square Matrix

#4:

Solutions:

$$a)\hspace{.2em}7$$

$$b)\hspace{.2em}x=-7, y=-5$$

#5:

Solutions:

$$a)\hspace{.2em}x=14, y=-23, z=0$$

$$b)\hspace{.2em}A ≠ B$$