Question

MULTIPLICATION OF MATRIX.

Plzz tell step by step..
Why it is not compatible..
Give reason tooo.

Answer 1

Given matrices,

$A=\left[\begin{array}{cc}2&3\\ 1&0\end{array}\right]\ \ \ ;\ \ \ B=\left[\begin{array}{c}2&3\end{array}\right]$

Here A is a 2 × 2 matrix and B is a 2 × 1 matrix.

So BA is not compatible because the no. of columns in B is not equal to the no. of rows in A.

This is an inevitable rule in the multiplication of two matrices.

$\boxed{\begin{minipage}{11.4cm}If A is an m\times n matrix and B is an n\times p matrix, then AB is an m\times p matrix.\\ \\ But if A is an m\times n matrix and B is a p\times q matrix, where n\neq p , then the matrix AB is not de\! \!fined.\end{minipage}}$

So on considering the multiplication of any two matrices, make sure that the no. of columns in the first matrix taken in the operation is equal to the no. of rows in the second matrix.

Here we're considering BA (not to be confused with AB). So BA will be possible if and only if the no. of columns in B is equal to the no. of rows in A.

But here the no. of columns in B is 1 while the no. of rows in A is 2. So BA is not compatible.

But AB is compatible, because the no. of columns in A is equal to the no. of rows in B. Both are 2 each.

$AB\ =\ \left[\begin{array}{cc}2&3\\ 1&0\end{array}\right]\cdot \left[\begin{array}{c}2\\ 3\end{array}\right]\ =\ \left[\begin{array}{c}2\cdot 2+3\cdot 3\\ 1\cdot 2+0\cdot 3\end{array}\right]\ =\ \left[\begin{array}{c}13\\ 2\end{array}\right]$

Answer 2

Answer:

Step-by-step

MULTIPLICATION OF MATRIX.  

Plzz tell step by step..

Why it is not compatible..

Give reason tooo.