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Matrix Addition and Subtraction Calculator

This calculator gives a detailed solution explaining the addition and subtraction of two matrices. Adding or subtracting two matrices is only possible if matrices are of the same size.

An m ร— n matrix is โ€‹โ€‹a table of numbers with m rows and n columns. Matrix elements are denoted as aij, where i is the row number, j is the column number.
The sum of matrices A and B, whose dimensions are the same, is called a matrix C of the same dimension as matrices A and B, whose elements are equal to the sums of elements of matrices A and B.



Matrix dimension: ร—
Matrix 1
A =
Matrix 2
B =


A B
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Examples of matrix addition and subtraction

Add two 2 ร— 3 matrices
C = A + B =
7 -1 0
6.45 2 5
+
0 -7.1 21
36 12 -9
=
7 + 0 -1 + (-7.1) 0 + 21
6.45 + 36 2 + 12 5 + (-9)
=
7 -8.1 21
42.45 14 -4

Solution

Given two matrices
A =
a11 a12 a13
a21 a22 a23
where,
a11 = 7
a12 = -1
a13 = 0
a21 = 6.45
a22 = 2
a23 = 5
B =
b11 b12 b13
b21 b22 b23
where,
b11 = 0
b12 = -7.1
b13 = 21
b21 = 36
b22 = 12
b23 = -9

Adding or subtracting two matrices is possible only if the matrices are of the same size.

When adding or subtracting m ร— n matrices A and B, we get a matrix C of the same m ร— n dimension

C =
a11 a12 a13
a21 a22 a23
+
b11 b12 b13
b21 b22 b23
=
a11 + b11 a12 + b12 a13 + b13
a21 + b21 a22 + b22 a23 + b23
Go to calculator
Add two 3 ร— 3 matrices
C = A + B =
0 4 9
-6 3 9.76
5 23 0
+
5 0 1
-1 -2 7
8.98 51 -3
=
0 + 5 4 + 0 9 + 1
-6 + (-1) 3 + (-2) 9.76 + 7
5 + 8.98 23 + 51 0 + (-3)
=
5 4 10
-7 1 16.76
13.98 74 -3

Solution

Given two matrices
A =
a11 a12 a13
a21 a22 a23
a31 a32 a33
where,
a11 = 0
a12 = 4
a13 = 9
a21 = -6
a22 = 3
a23 = 9.76
a31 = 5
a32 = 23
a33 = 0
B =
b11 b12 b13
b21 b22 b23
b31 b32 b33
where,
b11 = 5
b12 = 0
b13 = 1
b21 = -1
b22 = -2
b23 = 7
b31 = 8.98
b32 = 51
b33 = -3

Adding or subtracting two matrices is possible only if the matrices are of the same size.

When adding or subtracting m ร— n matrices A and B, we get a matrix C of the same m ร— n dimension

C =
a11 a12 a13
a21 a22 a23
a31 a32 a33
+
b11 b12 b13
b21 b22 b23
b31 b32 b33
=
a11 + b11 a12 + b12 a13 + b13
a21 + b21 a22 + b22 a23 + b23
a31 + b31 a32 + b32 a33 + b33
Go to calculator
Subtract two 2 ร— 3 matrices
C = A - B =
8 4 5
-9 0 7
-
4 23 -7
5 13 29
=
8 - 4 4 - 23 5 - (-7)
-9 - 5 0 - 13 7 - 29
=
4 -19 12
-14 -13 -22

Solution

Given two matrices
A =
a11 a12 a13
a21 a22 a23
where,
a11 = 8
a12 = 4
a13 = 5
a21 = -9
a22 = 0
a23 = 7
B =
b11 b12 b13
b21 b22 b23
where,
b11 = 4
b12 = 23
b13 = -7
b21 = 5
b22 = 13
b23 = 29

Adding or subtracting two matrices is possible only if the matrices are of the same size.

When adding or subtracting m ร— n matrices A and B, we get a matrix C of the same m ร— n dimension

C =
a11 a12 a13
a21 a22 a23
-
b11 b12 b13
b21 b22 b23
=
a11 - b11 a12 - b12 a13 - b13
a21 - b21 a22 - b22 a23 - b23
Go to calculator