Question

plz solve it...,...9 i​

Answer 1

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

Given that

$\rm :\longmapsto\:4A + 2I = \bigg[ \begin{matrix}14&8 \\ 4&6 \end{matrix} \bigg]$

We know, Identity matrix of order 2 × 2 is given by

$\rm :\longmapsto\:I = \bigg[ \begin{matrix}1&0 \\ 0&1 \end{matrix} \bigg]$

So, given equation reduces to

$\rm :\longmapsto\:4A + 2\bigg[ \begin{matrix}1&0 \\ 0&1 \end{matrix} \bigg] = \bigg[ \begin{matrix}14&8 \\ 4&6 \end{matrix} \bigg]$

$\rm :\longmapsto\:4A + \bigg[ \begin{matrix}2&0 \\ 0&2 \end{matrix} \bigg] = \bigg[ \begin{matrix}14&8 \\ 4&6 \end{matrix} \bigg]$

$\rm :\longmapsto\:4A = \bigg[ \begin{matrix}14&8 \\ 4&6 \end{matrix} \bigg] - \bigg[ \begin{matrix}2&0 \\ 0&2 \end{matrix} \bigg]$

$\rm :\longmapsto\:4A = \bigg[ \begin{matrix}14 - 2&8 - 0 \\ 4 - 0&6 - 2 \end{matrix} \bigg]$

$\rm :\longmapsto\:4A = \bigg[ \begin{matrix}12&8 \\ 4&4 \end{matrix} \bigg]$

$\bf :\longmapsto\:A = \bigg[ \begin{matrix}3&2 \\ 1&1 \end{matrix} \bigg]$

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

Given that

$\rm :\longmapsto\:2B + 3I = \bigg[ \begin{matrix}15&6 \\ 4&7 \end{matrix} \bigg]$

We know, Identity matrix of order 2 × 2 is given by

$\rm :\longmapsto\:I = \bigg[ \begin{matrix}1&0 \\ 0&1 \end{matrix} \bigg]$

So, given equation reduces to,

$\rm :\longmapsto\:2B + 3\bigg[ \begin{matrix}1&0 \\ 0&1 \end{matrix} \bigg] = \bigg[ \begin{matrix}15&6 \\ 4&7 \end{matrix} \bigg]$

$\rm :\longmapsto\:2B + \bigg[ \begin{matrix}3&0 \\ 0&3 \end{matrix} \bigg] = \bigg[ \begin{matrix}15&6 \\ 4&7 \end{matrix} \bigg]$

$\rm :\longmapsto\:2B = \bigg[ \begin{matrix}15&6 \\ 4&7 \end{matrix} \bigg] - \bigg[ \begin{matrix}3&0 \\ 0&3 \end{matrix} \bigg]$

$\rm :\longmapsto\:2B = \bigg[ \begin{matrix}15 - 3&6 \\ 4&7 - 3 \end{matrix} \bigg]$

$\rm :\longmapsto\:2B = \bigg[ \begin{matrix}12&6 \\ 4&4 \end{matrix} \bigg]$

$\bf :\longmapsto\:B = \bigg[ \begin{matrix}6&3 \\ 2&2 \end{matrix} \bigg]$

Additional Information :-

1. Addition of two matrices, A and B is possible only when both matrices A and B are of same order otherwise matrix addition is meaningless.

2. Subtraction of two matrices, A and B is possible only when both matrices A and B are of same order otherwise matrix subtraction is meaningless.

3. Matrix multiplication is possible only when number of columns of pre - multiplier is equal to number of rows of post - multiplier.