Multiplication Matrices :
In the first part we will look in to the multiplication of square matrices. In the next part you will learn to multiply different order matrices (e.g: 2x3 to 3x3).
Here we will multiply a 3x3 matrix (3 rows, 3 columns) to another 3x3 matrix (3 rows, 3 columns).
Matrix A
Matrix B
a11
a12
a13
a21
a22
a23
a31
a32
a33
x
b11
b12
b13
b21
b22
b23
b31
b32
b33
The resulting matrix will be a 3x3 matrix. We will have to calculate each cell of the result matrix separately. Let us assume the result to be X.
Step 1: To calculate x11
x11 is the cell where first row merges with first column. So in order to calculate the result we will use the first row of Matrix A and first column of Matrix B.
Result X
Matrix A
Matrix B
x11
x12
x13
x21
x22
x23
x31
x32
x33
=
a11
a12
a13
a21
a22
a23
a31
a32
a33
x
b11
b12
b13
b21
b22
b23
b31
b32
b33
Now x11 can be calculated as x11 = a11xb11 + a12xb21 + a13xb31
Step 2: To calculate x12
x12 is the cell where first row merges with second column. So in order to calculate the result we will use the first row of Matrix A and second column of Matrix B.
Result X
Matrix A
Matrix B
x11
x12
x13
x21
x22
x23
x31
x32
x33
=
a11
a12
a13
a21
a22
a23
a31
a32
a33
x
b11
b12
b13
b21
b22
b23
b31
b32
b33
Now x12 can be calculated as x12 = a11xb12 + a12xb22 + a13xb32
Following the same procedure we will have to calculate values for all cells.
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