Find the values of a, b, c and d if \[\left[ \begin{align} & a+b\,\,\,\,\,3 \\ & 5+c\,\,\,\,\,ab \\ \end{align} \right]=\left[ \begin{align} & 6\,\,\,\,d \\ & -1\,\,\,8 \\ \end{align} \right]\]

Find the values of a, b, c and d if

$\left[ (1) <img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-77cac3401696aea8c6e64f9a4e68e7d5_l3.png" height="73" width="125" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & a+b\,\,\,\,\,3 \\ & 5+c\,\,\,\,\,ab \\ \end{align*}" title="Rendered by QuickLaTeX.com"/> \right]=\left[ (2) <img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-76968cd058be7dc313e0c2e089aae33e_l3.png" height="70" width="84" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & 6\,\,\,\,d \\ & -1\,\,\,8 \\ \end{align*}" title="Rendered by QuickLaTeX.com"/> \right]$

Find the values of a, b, c and d if

Given

$\left[ (1) <img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f943dedc427a68d00fab787d10b96f3b_l3.png" height="73" width="125" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & a+b\,\,\,\,\,3 \\ & 5+c\,\,\,\,\,ab \\ \end{align*}" title="Rendered by QuickLaTeX.com"/> \right]=\left[ (2) <img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0def0aa4f75e62893bac5316b0a114f5_l3.png" height="70" width="84" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & 6\,\,\,\,d \\ & -1\,\,\,8 \\ \end{align*}" title="Rendered by QuickLaTeX.com"/> \right]$

Comparing the corresponding terms, we get

$\begin{array}{*{35}{l}} 3\text{ }=\text{ }d \\ d\text{ }=\text{ }3 \\ \end{array}$

Also we have

$\begin{array}{*{35}{l}} 5\text{ }+\text{ }c\text{ }=\text{ }-1 \\ c\text{ }=\text{ }-1\text{ }\text{ }5 \\ c\text{ }=\text{ }-6 \\ \end{array}$

Also we have,

$a\text{ }+\text{ }b\text{ }=\text{ }6\text{ }and\text{ }a\text{ }b\text{ }=\text{ }8$

we know that,

$\begin{array}{*{35}{l}} {{\left( a\text{ }\text{ }b \right)}^{2}}~=\text{ }{{\left( a\text{ }+\text{ }b \right)}^{2}}~\text{ }4\text{ }ab \\ {{\left( 6 \right)}^{2}}~\text{ }32\text{ }=\text{ }36\text{ }\text{ }32\text{ }=\text{ }4\text{ }=\text{ }{{\left( \pm \text{ }2 \right)}^{2}} \\ a\text{ }\text{ }b\text{ }=\text{ }\pm \text{ }2 \\ If\text{ }a\text{ }\text{ }b\text{ }=\text{ }2 \\ a\text{ }+\text{ }b\text{ }=\text{ }6 \\ \end{array}$

Adding the above two equations we get

$\begin{array}{*{35}{l}} 2a\text{ }=\text{ }4 \\ a\text{ }=\text{ }4/2 \\ a\text{ }=\text{ }2 \\ b\text{ }=\text{ }6\text{ }\text{ }4 \\ b\text{ }=\text{ }2 \\ \end{array}$

Again we have

$a\text{ }\text{ }b\text{ }=\text{ }-2$

And

$a\text{ }+\text{ }b\text{ }=\text{ }6$

Adding above equations we get

$\begin{array}{*{35}{l}} 2a\text{ }=\text{ }4 \\ a\text{ }=\text{ }4/2 \\ a\text{ }=\text{ }2 \\ \end{array}$

Also,

$b\text{ }=\text{ }6\text{ }\text{ }2\text{ }=\text{ }4$

$a\text{ }=\text{ }2\text{ }and\text{ }b\text{ }=\text{ }4$

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