Question

2. Find the value of , given that 2 = , = [ 2 12 0 1 ] and = [ 4 0 1 ] matrix please answer my points are getting waisted
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Answer 1

Correct question :-

Find the value of x, given that A² = B, A = [2 12 0 1] and B = [4 x 0 1].

Given :-

$\sf{\bullet\ A^2=B}$

$\sf{\bullet\ A=\left[\begin{array}{c c}2 & 12 \\ 0 & 1 \end{array}\right]}$

$\sf{\bullet\ B=\left[\begin{array}{c c}4 & x \\ 0 & 1 \end{array}\right]}$

To Find :-

The value of x.

Solution :-

$\sf{A=\left[\begin{array}{c c}2 & 12 \\ 0 & 1 \end{array}\right]\:\:\:\:\:\:\:\:\:\: (given)}$

$\sf{A^2=B}$

LHS :

$\sf{A^2=\left[\begin{array}{c c}2 & 12 \\ 0 & 1 \end{array}\right]\left[\begin{array}{c c}2 & 12 \\ 0 & 1 \end{array}\right]}$

$\hookrightarrow \sf{A^2=\left[\begin{array}{c c}2(2 \times 2)+(12 \times 0) & (2 \times 12)+(12 \times 1) \\ (0\times2)+(1\times0) & (0\times12)+(1\times1) \end{array}\right]}$

$\hookrightarrow \sf{A^2=\left[\begin{array}{c c}4+0 &24+12 \\ 0+0 & 0+1 \end{array}\right]}$

$\hookrightarrow \sf{A^2=\left[\begin{array}{c c}4 &36 \\ 0 & 1 \end{array}\right]}$

Equating with RHS :

$\hookrightarrow \sf{\left[\begin{array}{c c}4 &36 \\ 0 & 1 \end{array}\right]=B}$

$\hookrightarrow \sf{\left[\begin{array}{c c}4 &36 \\ 0 & 1 \end{array}\right]=\left[\begin{array}{c c}4 &x \\ 0 & 1 \end{array}\right]}$

Comparing the corresponding elements of the equal matrices, we get that

$\large\boxed{\bold{x=36}}$