Question

If A=[(1 -2 1)(2 1 3)] and B =[(2 1)(3 2)(1 1) ,write down the matrix AB .would it be possible to find the product AB? if a computer it and if not give reason​

Answer 1

Solution.

Given -

$\implies\left \tt A=\left[\begin{array}{ccc}\tt1&\tt-2&\tt1\\ \tt2&\tt1&\tt3\end{array}\right]$

$\implies\left \tt B=\left[\begin{array}{cc}\tt2&\tt1\\ \tt3&\tt2\\ \tt1&\tt1\end{array}\right]$

⊕ We have to find the matrix AB.

$\implies\left \tt AB=\left[\begin{array}{ccc}\tt1&\tt-2&\tt1\\ \tt2&\tt1&\tt3\end{array}\right]\left[\begin{array}{cc}\tt2&\tt1\\ \tt3&\tt2\\ \tt1&\tt1\end{array}\right]$

Here,

> Order of matrix A = 2 × 3

> Order of matrix B = 3 × 2

> Order of matrix AB = 2 × 2

$\implies \left\tt AB= \left[\begin{array}{cc}\tt( 1\times2-2\times3+1\times1) &\tt (1\times1-2\times2+1\times1)\\ \tt(2\times2+1\times3+3\times1)& \tt(2\times1+1\times2+3\times1)\end{array}\right]$

$\implies \left\tt AB= \left[\begin{array}{cc}\tt(2-6+1) &\tt (1-4+1)\\ \tt(4+3+3)& \tt(2+2+3)\end{array}\right]$

$\implies \left\tt AB= \left[\begin{array}{cc}\tt-3 &\tt -2\\ \tt10& \tt7\end{array}\right]\ \ \bigstar$

⊕ So, we have found the matrix AB.

Yes, it is possible to find the matrix BA. This is because, the number of columns on matrix B is equal to the number of rows of matrix A.

> Order of matrix B = 3 × 2

> Order of matrix A = 2 × 3

> Order of matrix BA = 3 × 3

$\implies\left \tt BA=\left[\begin{array}{cc}\tt2&\tt1\\ \tt3&\tt2\\ \tt1&\tt1\end{array}\right]\left[\begin{array}{ccc}\tt1&\tt-2&\tt1\\ \tt2&\tt1&\tt3\end{array}\right]$

$\implies\left \tt BA=\left[\begin{array}{ccc}\tt(2\times1+1\times2)&\tt(-2\times2+1\times1)&\tt(2\times1+1\times3)\\ \tt(3\times1+2\times2)&\tt(-3\times2+2\times1)&\tt(3\times1+2\times3)\\ \tt(1\times1+1\times2)&\tt(-1\times2+1\times1)&\tt(1\times1+1\times3)\end{array}\right]$

$\implies\left \tt BA=\left[\begin{array}{ccc}\tt(2+2)&\tt(-4+1)&\tt(2+3)\\ \tt(3+4)&\tt(-6+2)&\tt(3+6)\\ \tt(1+2)&\tt(-2+1)&\tt(1+3)\end{array}\right]$

$\implies\left \tt BA=\left[\begin{array}{ccc}\tt4&\tt-3&\tt5\\ \tt7&\tt-4&\tt9\\ \tt3&\tt-1&\tt4\end{array}\right]\ \ \bigstar$

Therefore, matrix BA is also calculated!

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Answer 2

Answer:

https://brainly.in/question/42296877