How to Add and Subtract Matrices? (+FREE Worksheet!)

How to Add and Subtract Matrices? (+FREE Worksheet!) is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.

Adding and Subtracting Matrices – Example 1:

(begin{bmatrix} 2 & -5 & -3 end{bmatrix}+ begin{bmatrix}1 & -2 & -3 end{bmatrix})

Solution:

Add the elements in the matching positions: (begin{bmatrix} 2+1 & -5+(-2) & -3+(-3) end{bmatrix}= begin{bmatrix}3 & -7 & -6 end{bmatrix})

The Absolute Best Books to Ace Pre-Algebra to Algebra II

The Ultimate Algebra Bundle 2026 From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Adding and Subtracting Matrices – Example 2:

(begin{bmatrix}3 & 6 \-1 & -3 \-5 & -1end{bmatrix}+ begin{bmatrix}0 & -1 \6 & 0 \2 & 3end{bmatrix} )

Solution:

Add the elements in the matching positions: (begin{bmatrix}3+0 & 6+(-1) \-1+6 & -3+0 \-5+2 & -1+3end{bmatrix} = begin{bmatrix}3 & 5 \5 & -3 \-3 & 2end{bmatrix} )

Adding and Subtracting Matrices – Example 3:

(begin{bmatrix}2 & -1 \0 & 1 end{bmatrix}+begin{bmatrix}3 & 1 \5 & -2 end{bmatrix})

Solution:

Add the elements in the matching positions: (begin{bmatrix}2+3 & -1+1 \0+5 & 1+(-2) end{bmatrix}=begin{bmatrix}5 & 0 \5 & -1 end{bmatrix})

Adding and Subtracting Matrices – Example 4:

(begin{bmatrix}-1 & 2 \3 & 4 \0 & -2end{bmatrix}- begin{bmatrix}5 & -2 \6 & 1 \-3 & 4end{bmatrix} )

Solution:

Subtract the elements in the matching positions: (begin{bmatrix}-1-5 & 2-(-2) \3-6 & 4-1 \0-(-3) & -2-4end{bmatrix}= begin{bmatrix}-6 & 4 \-3 & 3 \3 & -6end{bmatrix})

Exercises for Adding and Subtracting Matrices

1. (color{blue}{begin{bmatrix}6 & 8 \-14 & 33 end{bmatrix}-begin{bmatrix}12 & 5 \-27 & -8 end{bmatrix}})
2. (color{blue}{begin{bmatrix}12 & 21 \-17 & 33 end{bmatrix}-begin{bmatrix}5& -8 \2 & 19 end{bmatrix}})
3. (color{blue}{begin{bmatrix}-5 & 2& -2 \4 & -2&0 end{bmatrix}-begin{bmatrix}6 & -5&-6 \1 & 3&-3 end{bmatrix}})
4. (color{blue}{begin{bmatrix}-6r+t \-r\6s end{bmatrix}+begin{bmatrix}6r \-4t\-3r+2 end{bmatrix}})
5. (color{blue}{begin{bmatrix}16 & -4 \-38 & 24 end{bmatrix}+begin{bmatrix}9 & -6 \5& 2 end{bmatrix}})
6. (color{blue}{begin{bmatrix}18 & -5 \-32 & 14 end{bmatrix}+begin{bmatrix}11& -6 \7 & 2 end{bmatrix}})
7. (color{blue}{begin{bmatrix}-4n & n+m \-2n & -4mend{bmatrix}+begin{bmatrix}4 & -5 \3 & 0 end{bmatrix}})
8. (color{blue}{begin{bmatrix}z-5 \-6\-1-6z\3y end{bmatrix}+begin{bmatrix}-3y\3z\5+z\4z end{bmatrix}})

Adding and Subtracting Matrices

Solve.

1. (color{blue}{begin{bmatrix}-6 & 3 \13 & 41 end{bmatrix}})
2. (color{blue}{begin{bmatrix}7 & 29 \-19 & 14 end{bmatrix}})
3. (color{blue}{begin{bmatrix}-11 & 7&4 \3 & -5&3 end{bmatrix}})
4. (color{blue}{begin{bmatrix}t \-r-4t\6s-3r+2 end{bmatrix}} )
5. (color{blue}{begin{bmatrix}25 & -10 \-33 & 26 end{bmatrix}})
6. (color{blue}{begin{bmatrix}29 & -11 \-25 & 16 end{bmatrix}})
7. (color{blue}{begin{bmatrix}-4n+4 & n+m-5 \-2n+3 & -4mend{bmatrix}})
8. (color{blue}{begin{bmatrix}z-5-3y \-6+3z\4-5z\3y+4z end{bmatrix}} )

The Greatest Books for Students to Ace the Algebra

Pre-Algebra Exercise Book A Comprehensive Workbook + PreAlgebra Practice Tests

Download

$29.99 Original price was: $29.99.$16.99Current price is: $16.99.