About Introduction to Matrices:
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
#1:
Instructions: state the order.
$$a)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}5 & -1 & 3\\ 3 & 7 & 0\end{array}\right]$$
$$b)\hspace{.2em}$$ $$\left[ \begin{array}{ccc}-9 & 19 & 17\\ 2 & 3 & 0 \\ 1 & -1 & 5\end{array}\right]$$
Watch the Step by Step Video Lesson View the Written Solution
#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
$$b)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}5 & 6 \\ 1 & -1 \\ 7 & 3\end{array}\right]$$
Watch the Step by Step Video Lesson View the Written Solution
#3:
Instructions: what is element: a2,3
$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}5 & 6 \\ 1 & -1 \\ 7 & 3\end{array}\right]$$
Instructions: give the best answer.
b) What type of matrix has the same number of rows as columns?
Watch the Step by Step Video Lesson View the Written Solution
#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?
$$b)\hspace{.2em}$$
$$A=\left[ \begin{array}{cc}-3 & 1 \\ 6 & x + 5\end{array}\right]$$ $$B=\left[ \begin{array}{cc}y + 2 & 1 \\ 6 & -2\end{array}\right]$$Watch the Step by Step Video Lesson View the Written Solution
#5:
Instructions: find x, y, and z such that A = B.
$$a)\hspace{.2em}$$
$$A=\left[ \begin{array}{ccc}-1 & 5 & 9 \\ x - 1 & y + 2 & 4\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}-1 & 5 & 9 \\ 13 & -21 & z + 4\end{array}\right]$$$$b)\hspace{.2em}$$
$$A=\left[ \begin{array}{ccc}3 & 5 & 11 \\ x + 1 & y - 7 & 7\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}3 & 11 & 5 \\ -14 & 12 & z - 9\end{array}\right]$$Watch the Step by Step Video Lesson View the Written Solution
Written Solutions:
#1:
Solutions:
a) 2 x 3
b) 3 x 3
Watch the Step by Step Video Lesson
#2:
Solutions:
a) 3 x 5
b) 6
Watch the Step by Step Video Lesson
#3:
Solutions:
a) Doesn't exist
b) Square Matrix
Watch the Step by Step Video Lesson
#4:
Solutions:
$$a)\hspace{.2em}7$$
$$b)\hspace{.2em}x=-7, y=-5$$
Watch the Step by Step Video Lesson
#5:
Solutions:
$$a)\hspace{.2em}x=14, y=-23, z=0$$
$$b)\hspace{.2em}A ≠ B$$
