Question

solve it
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Answer 1

Answer:

Step-by-step explanation:

We have,

$\bb{A=\left[\begin{array}{cc}1&9\\0&\dfrac{1}{4}\end{array}\right] \,\,and\,\,\,}\bb{B=\left[\begin{array}{cc}2&x\\0&1\end{array}\right] }$

Now,

$\bb{4A=4\left[\begin{array}{cc}1&9\\0&\dfrac{1}{4}\end{array}\right] =\left[\begin{array}{cc}4&36\\0&1\end{array}\right] }$

And,

$\bb{B^2=\left[\begin{array}{cc}2&x\\0&1\end{array}\right]\cdot\left[\begin{array}{cc}2&x\\0&1\end{array}\right] }$

$\bb{\implies\,B^2=\left[\begin{array}{cc}(2)(2)+(x)(0)&(2)(x)+(2)(1)\\\\(0)(2)+(0)(1)&(0)(x)+(1)(1)\end{array}\right]}$

$\bb{\implies\,B^2=\left[\begin{array}{cc}4&2x+2\\0&1\end{array}\right]}$

According to the given condition,

$\sf{\red{4A=B^2}}$

$\sf{\implies\left[\begin{array}{cc}4&36\\0&1\end{array}\right]=\left[\begin{array}{cc}4&2x+2\\0&1\end{array}\right]}$

On comparing, we get,

$\sf{2x+2=36}$

$\sf{\implies\,2x=36-2}$

$\sf{\implies\,2x=34}$

$\sf{\implies\,x=17}$