Question

➟ Give necessary calculations
➟ Quality answer needed​

Answer 1

A×B=

l-3 20 7 l

l-8 1 15 l

l-9 5 -2 l

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:\begin{gathered}\sf A=\left[\begin{array}{ccc}7&2&1\\2&0&5\\3&2&4\end{array}\right]\end{gathered}$

$\rm :\longmapsto\:\begin{gathered}\sf B=\left[\begin{array}{ccc}1&3&0\\4&0&5\\2&1&3\end{array}\right]\end{gathered}$

and

$\rm :\longmapsto\:\begin{gathered}\sf C=\left[\begin{array}{cc}2&1\\1&2\\4&4\end{array}\right]\end{gathered}$

To Find :-

$\rm :\longmapsto\:A \times B + C$

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:\begin{gathered}\sf A=\left[\begin{array}{ccc}7&2&1\\2&0&5\\3&2&4\end{array}\right]\end{gathered}$

and

$\rm :\longmapsto\:\begin{gathered}\sf B=\left[\begin{array}{ccc}1&3&0\\4&0&5\\2&1&3\end{array}\right]\end{gathered}$

Consider

$\red{\bf :\longmapsto\:A \times B}$

$\rm \: = \: \: \begin{gathered}\sf \left[\begin{array}{ccc}7&2&1\\2&0&5\\3&2&4\end{array}\right]\end{gathered}\begin{gathered}\sf \left[\begin{array}{ccc}1&3&0\\4&0&5\\2&1&3\end{array}\right]\end{gathered}$

$\rm \: = \: \: \begin{gathered}\sf \left[\begin{array}{ccc}7 + 8 + 2&21 + 0 + 1&0 + 10 + 3\\2 + 0 + 10&6 + 0 + 5&0 + 0 + 15\\3 + 8 + 8&9 + 0 + 4&0 + 10 + 12\end{array}\right]\end{gathered}$

$\rm \: = \: \: \begin{gathered}\sf \left[\begin{array}{ccc}17&22&13\\12&11&15\\19&13&22\end{array}\right]\end{gathered}$

$\bf\implies \:A \times B = \: \: \begin{gathered}\sf \left[\begin{array}{ccc}17&22&13\\12&11&15\\19&13&22\end{array}\right]\end{gathered}$

Now,

Consider,

$\purple{\bf :\longmapsto\:A \times B + C}$

$\rm \: = \: \: \begin{gathered}\sf \left[\begin{array}{ccc}17&22&13\\12&11&15\\19&13&22\end{array}\right]\end{gathered} + \begin{gathered}\sf \left[\begin{array}{cc}2&1\\1&2\\4&4\end{array}\right]\end{gathered}$

$\rm \: = \: \: which \: is \: meaningless$

Because matrix addition is possible only when order of the matrices are same.

$\bf\implies \:A \times B + C \: is \: not \: defined.$

Additional Information :-

1. Matrix multiplication of two matrices A and Bis defined only when number of columns of pre - multiplier is equals to number of rows of post multiplier otherwise matrix multiplication is not defined.

2. Matrix multiplication may or may not be Commutative. i.e. AB may or not be equal to BA

3. Matrix multiplication is Associative. i.e. (AB)C = A(BC).

4. Matrix multiplication is Distributive. i.e. A(B + C) = AB + AC.