HOW TO MULTIPLY MATRICES

The product of matrix AB is determined by multiplying every row matrix of A by the column matrix of B.

If A  =  [a_ij]_mxn and B  =  [b_ij]_{nxp then the product matrix AB is defined by} 

Multiplying Row Matrix by Column Matrix

Question 1 :

Find the product of the matrices, if exists.

Solution :

Order of matrix A is 1 x 2 and order of matrix B is 2 x 1.

The order of matrix AB is 1 x 1.

Multiplying a Column Matrix by Row Matrix

Question 2 :

then find AB.

Solution :

Order of matrix A is 3 x 1.

Order of matrix B is 1 x 3

Order of matrix AB is 3 x 3.

Multiplying Matrices of Different Dimensions

Question 3 :

Find the product of the given matrices.

Solution :

By multiplying the first row of matrix A by the columns of matrix B, we get row 1 of resultant matrix AB.

By multiplying the second row of matrix A by the columns of matrix B, we get row 2 of resultant matrix AB.

Order of matrix A is 2 x 3, order of matrix B is 3 x 2.

So, the order of matrix AB will be 2 x 2.

By doing simplification, we get the result.

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