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 }
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.
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.
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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