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Matrix Addition and Subtraction Operations

HomeAlgebraMatrices and DeterminantsElementary Row Operations

The rules for matrix addition are very simple:

Add two or more matrices of the same order by summing their corresponding array elements.

Matrix Addition:

2×2

Column 1

Column 2

Row 1:

4

+√9

Row 2:

-3

5

Matrix A

2×2

Column 1

Column 2

Row 1:

a11

a12

Row 2:

a21

a22

Address Elements Matrix A

2×2

Column 1

Column 2

Row 1:

2

1

Row 2:

3

2

Matrix B

2×2

Column 1

Column 2

Row 1:

b11

b12

Row 2:

b21

b22

Address Elements Matrix B

a11 + b11 = 4 + 2 = 6

a12 + b12 = 3 + 1 = 4

a21 + b21 = -3 + 3 = 0

a22 + b22 = 5 + 2 = 7

2×2

Column 1

Column 2

Row 1:

6

4

Row 2:

0

7

Result Matrix A + B

Matrix Subtraction:

The rules for matrix subtraction are very simple:

Subtract the corresponding array elements of two or more matrices of the same order.

2×2

Column 1

Column 2

Row 1:

4

+√9

Row 2:

-3

5

Matrix A

2×2

Column 1

Column 2

Row 1:

a11

a12

Row 2:

a21

a22

Address Elements Matrix A

2×2

Column 1

Column 2

Row 1:

2

1

Row 2:

3

2

Matrix B

2×2

Column 1

Column 2

Row 1:

b11

b12

Row 2:

b21

b22

Address Elements Matrix B

a11 – b11 = 4 – 2 = 2

a12 – b12 = 3 – 1 = 2

a21 – b21 = -3 – 3 = -6

a22 – b22 = 5 – 2 = 3

2×2

Column 1

Column 2

Row 1:

2

2

Row 2:

-6

3

Result Matrix A − B

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