Matrix Operations

Topic 2 - Operations on Matrices

Matrix Addition

Matrix addition means adding the corresponding elements of two matrices. It is only possible when both matrices have the same order (same number of rows and columns).

Example:

1 2
3 4

5 6
7 8

6 8
10 12

Each element is added: (1+5), (2+6), (3+7), (4+8)

Scalar Multiplication

In scalar multiplication, each element of a matrix is multiplied by a constant number.

Example:

1 2
3 4

2 4
6 8

Each element is multiplied by 2.

Matrix Multiplication

Matrix multiplication is done by multiplying rows of the first matrix with columns of the second matrix.

Example:

1 2
3 4

5 6
7 8

19 22
43 50

Step:
First element → (1×5 + 2×7) = 19
Second element → (1×6 + 2×8) = 22

Important Notes

Addition possible only if order is same
Multiplication is not commutative (AB ≠ BA)
Number of columns of first matrix must equal rows of second
Always follow row × column rule