Sec 4 E-Math · Matrices

Adding and subtracting matrices questions with answers

Practice questions on adding and subtracting matrices, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

$A = \begin{pmatrix} 3 & -3 \\ 7 & 5 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 4 \\ -4 & -5 \end{pmatrix}$ . Find $A + B$ .

Step 1 of 3

Row 1: add the elements in the same position

Column 1:

3 + 2 = 5

Column 2:

-3 + 4 = 1

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Questions

Question 1Adding
$A = \begin{pmatrix} 7 & 7 \\ -1 & -2 \end{pmatrix}$ and $B = \begin{pmatrix} 7 & -1 \\ 6 & 4 \end{pmatrix}$ . Find $A + B$ .
Show the worked solution
1. Step 1: Row 1: add the elements in the same positionColumn 1: $7 + 7 = 14$ Column 2: $7 + (-1) = 6$
2. Step 2: Row 2: add the elements in the same positionColumn 1: $-1 + 6 = 5$ Column 2: $-2 + 4 = 2$
3. Step 3: Write the answer as a matrix $A + B = \begin{pmatrix} 14 & 6 \\ 5 & 2 \end{pmatrix}$
Question 2Adding
$A = \begin{pmatrix} 2 & 6 \\ 1 & -3 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 6 \\ 7 & -1 \end{pmatrix}$ . Find $A + B$ .
Show the worked solution
1. Step 1: Row 1: add the elements in the same positionColumn 1: $2 + 2 = 4$ Column 2: $6 + 6 = 12$
2. Step 2: Row 2: add the elements in the same positionColumn 1: $1 + 7 = 8$ Column 2: $-3 + (-1) = -4$
3. Step 3: Write the answer as a matrix $A + B = \begin{pmatrix} 4 & 12 \\ 8 & -4 \end{pmatrix}$
Question 3Subtracting, any order
$A = \begin{pmatrix} -4 \\ -4 \end{pmatrix}$ and $B = \begin{pmatrix} 1 \\ -5 \end{pmatrix}$ . Find $A - B$ .
Show the worked solution
1. Step 1: Row 1: subtract the elements in the same position $-4 - 1 = -5$
2. Step 2: Row 2: subtract the elements in the same position $-4 - (-5) = 1$
3. Step 3: Write the answer as a matrix $A - B = \begin{pmatrix} -5 \\ 1 \end{pmatrix}$
Question 4Subtracting, any order
$A = \begin{pmatrix} 2 & 1 & -5 \\ -3 & -6 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & -2 & -1 \\ -2 & 9 & 4 \end{pmatrix}$ . Find $A - B$ .
Show the worked solution
1. Step 1: Row 1: subtract the elements in the same positionColumn 1: $2 - 3 = -1$ Column 2: $1 - (-2) = 3$ Column 3: $-5 - (-1) = -4$
2. Step 2: Row 2: subtract the elements in the same positionColumn 1: $-3 - (-2) = -1$ Column 2: $-6 - 9 = -15$ Column 3: $1 - 4 = -3$
3. Step 3: Write the answer as a matrix $A - B = \begin{pmatrix} -1 & 3 & -4 \\ -1 & -15 & -3 \end{pmatrix}$
Question 5Three matrices
$A = \begin{pmatrix} 4 & 2 \\ 8 & 8 \end{pmatrix}$ , $B = \begin{pmatrix} 5 & -1 \\ -3 & 7 \end{pmatrix}$ and $C = \begin{pmatrix} 5 & 6 \\ 1 & -3 \end{pmatrix}$ . Find $A + B - C$ .
Show the worked solution
1. Step 1: Row 1: combine the elements in the same positionColumn 1: $4 + 5 - 5 = 4$ Column 2: $2 + (-1) - 6 = -5$
2. Step 2: Row 2: combine the elements in the same positionColumn 1: $8 + (-3) - 1 = 4$ Column 2: $8 + 7 - (-3) = 18$
3. Step 3: Write the answer as a matrix $A + B - C = \begin{pmatrix} 4 & -5 \\ 4 & 18 \end{pmatrix}$
Question 6Three matrices
$A = \begin{pmatrix} 4 & 5 \\ 4 & -4 \end{pmatrix}$ , $B = \begin{pmatrix} 4 & 7 \\ 5 & 1 \end{pmatrix}$ and $C = \begin{pmatrix} 5 & 1 \\ 2 & 4 \end{pmatrix}$ . Find $A + B - C$ .
Show the worked solution
1. Step 1: Row 1: combine the elements in the same positionColumn 1: $4 + 4 - 5 = 3$ Column 2: $5 + 7 - 1 = 11$
2. Step 2: Row 2: combine the elements in the same positionColumn 1: $4 + 5 - 2 = 7$ Column 2: $-4 + 1 - 4 = -7$
3. Step 3: Write the answer as a matrix $A + B - C = \begin{pmatrix} 3 & 11 \\ 7 & -7 \end{pmatrix}$

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Worked example

A = \begin{pmatrix} 3 & -3 \\ 7 & 5 \end{pmatrix}

and

B = \begin{pmatrix} 2 & 4 \\ -4 & -5 \end{pmatrix}

. Find

A + B

Step 1 of 3

Row 1: add the elements in the same position

Column 1:

3 + 2 = 5

Column 2:

-3 + 4 = 1

Questions

Question 1Adding

$A = \begin{pmatrix} 7 & 7 \\ -1 & -2 \end{pmatrix}$ and $B = \begin{pmatrix} 7 & -1 \\ 6 & 4 \end{pmatrix}$ . Find $A + B$ .

Show the worked solution

Step 1: Row 1: add the elements in the same positionColumn 1: $7 + 7 = 14$ Column 2: $7 + (-1) = 6$
Step 2: Row 2: add the elements in the same positionColumn 1: $-1 + 6 = 5$ Column 2: $-2 + 4 = 2$
Step 3: Write the answer as a matrix $A + B = \begin{pmatrix} 14 & 6 \\ 5 & 2 \end{pmatrix}$

Question 2Adding

$A = \begin{pmatrix} 2 & 6 \\ 1 & -3 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 6 \\ 7 & -1 \end{pmatrix}$ . Find $A + B$ .

Show the worked solution

Step 1: Row 1: add the elements in the same positionColumn 1: $2 + 2 = 4$ Column 2: $6 + 6 = 12$
Step 2: Row 2: add the elements in the same positionColumn 1: $1 + 7 = 8$ Column 2: $-3 + (-1) = -4$
Step 3: Write the answer as a matrix $A + B = \begin{pmatrix} 4 & 12 \\ 8 & -4 \end{pmatrix}$

Question 3Subtracting, any order

$A = \begin{pmatrix} -4 \\ -4 \end{pmatrix}$ and $B = \begin{pmatrix} 1 \\ -5 \end{pmatrix}$ . Find $A - B$ .

Show the worked solution

Step 1: Row 1: subtract the elements in the same position $-4 - 1 = -5$
Step 2: Row 2: subtract the elements in the same position $-4 - (-5) = 1$
Step 3: Write the answer as a matrix $A - B = \begin{pmatrix} -5 \\ 1 \end{pmatrix}$

Question 4Subtracting, any order

$A = \begin{pmatrix} 2 & 1 & -5 \\ -3 & -6 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & -2 & -1 \\ -2 & 9 & 4 \end{pmatrix}$ . Find $A - B$ .

Show the worked solution

Step 1: Row 1: subtract the elements in the same positionColumn 1: $2 - 3 = -1$ Column 2: $1 - (-2) = 3$ Column 3: $-5 - (-1) = -4$
Step 2: Row 2: subtract the elements in the same positionColumn 1: $-3 - (-2) = -1$ Column 2: $-6 - 9 = -15$ Column 3: $1 - 4 = -3$
Step 3: Write the answer as a matrix $A - B = \begin{pmatrix} -1 & 3 & -4 \\ -1 & -15 & -3 \end{pmatrix}$

Question 5Three matrices

$A = \begin{pmatrix} 4 & 2 \\ 8 & 8 \end{pmatrix}$ , $B = \begin{pmatrix} 5 & -1 \\ -3 & 7 \end{pmatrix}$ and $C = \begin{pmatrix} 5 & 6 \\ 1 & -3 \end{pmatrix}$ . Find $A + B - C$ .

Show the worked solution

Step 1: Row 1: combine the elements in the same positionColumn 1: $4 + 5 - 5 = 4$ Column 2: $2 + (-1) - 6 = -5$
Step 2: Row 2: combine the elements in the same positionColumn 1: $8 + (-3) - 1 = 4$ Column 2: $8 + 7 - (-3) = 18$
Step 3: Write the answer as a matrix $A + B - C = \begin{pmatrix} 4 & -5 \\ 4 & 18 \end{pmatrix}$

Question 6Three matrices

$A = \begin{pmatrix} 4 & 5 \\ 4 & -4 \end{pmatrix}$ , $B = \begin{pmatrix} 4 & 7 \\ 5 & 1 \end{pmatrix}$ and $C = \begin{pmatrix} 5 & 1 \\ 2 & 4 \end{pmatrix}$ . Find $A + B - C$ .

Show the worked solution

Step 1: Row 1: combine the elements in the same positionColumn 1: $4 + 4 - 5 = 3$ Column 2: $5 + 7 - 1 = 11$
Step 2: Row 2: combine the elements in the same positionColumn 1: $4 + 5 - 2 = 7$ Column 2: $-4 + 1 - 4 = -7$
Step 3: Write the answer as a matrix $A + B - C = \begin{pmatrix} 3 & 11 \\ 7 & -7 \end{pmatrix}$