Question

Please, Solve the above attachment !!!


$\large \bold \red{Dont \: Spam \: !!}$
​

Answer 1

Step-by-step explanation:

★ Given :-

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

$\large \bold \red{A} = \left[\begin{array}{ccc}3 & 0 \\ 5 & 1 \end{array} \right] \huge \:\:\& \:\: \large \bold \red{B} = \left[\begin{array}{ccc}-4 & 2 \\ 1 & 0 \end{array} \right]$

⠀⠀⠀⠀⠀⠀

★ To Find :-

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\mapsto\large\bold\pink{A {}^{2} -2AB + B {}^{2} }$

⠀⠀⠀⠀⠀⠀

★ Solution :-

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

$\ \bold \red{For (1) } \mapsto\bold{A {}^{2} } \\ \\ \ \bold A {}^{2} =\left[\begin{array}{ccc}3 & 0 \\ 5 & 1 \end{array} \right] \left[\begin{array}{ccc}3 & 0 \\ 5 & 1 \end{array} \right] =\left[\begin{array}{ccc}9 + 0 & 0 + 0 \\ 15 + 5 & 5 + 1 \end{array} \right] =\left[\begin{array}{ccc}9 & 0 \\ 20 & 1 \end{array} \right] \\ \\ \bold \red{For (2) } \: \mapsto \bold{AB} \\ \\ \bold{AB = \left[\begin{array}{ccc}3 & 0 \\ 5 & 1 \end{array} \right]\left[\begin{array}{ccc}-4 & 2 \\ 1 & 0\end{array} \right] = \left[\begin{array}{ccc}-12 + 0 & 6 + 0 \\ - 20 + 1 & 10 + 0 \end{array} \right] =\left[\begin{array}{ccc}-12 & 6 \\ - 19 & 10 \end{array} \right] } \\ \\ \large \bold \red{For (3) } \mapsto \bold{B {}^{2} } \\ \\ \bold{B {}^{2} =\left[\begin{array}{ccc}-4 & 2 \\ 1 & 0 \end{array} \right] \left[\begin{array}{ccc}-4 & 2 \\ 1 & 0\end{array} \right] = \left[\begin{array}{ccc}-16 + 2 & - 8 + 0 \\ - 4 + 0 & 2 + 0 \end{array} \right] = \left[\begin{array}{ccc}18 & - 8 \\ - 4 & 2 \end{array} \right]}$

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

★ Therefore,⠀

⠀⠀⠀

⠀⠀⠀⠀⠀⠀

$\mapsto\large \bold \pink{A {}^{2} - 2 AB +B {}^{2} } = \bold{\left[\begin{array}{ccc}9 & 0 \\ 20 & 1 \end{array} \right] - 2}\left[\begin{array}{ccc} - 12 & 6 \\ - 19 & 10 \end{array} \right] + \left[\begin{array}{ccc}18 & - 8 \\ - 4 & 2 \end{array} \right] \\ \\ = \left[\begin{array}{ccc}9 & 0 \\ \large 20& 1 \end{array} \right] - \left[\begin{array}{ccc} - 24 & 12 \\ - 38 &20 \end{array} \right] + \left[\begin{array}{ccc}18 & - 8 \\ - 4 & 2 \\ \end{array} \right] \\ \\ \mapsto \large \bold\red{\left[\begin{array}{ccc}51 & - 20 \\ 54& - 17 \end{array} \right]}$

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

★ Hence,

⠀⠀⠀⠀⠀⠀

$\rightarrow\large \bold \red{The Value = \pink{\left[\begin{array}{ccc}51 & - 20 \\ 54 & - 1 7\end{array} \right]}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\colorbox{pink}{Hope lt'z Help You ❥ }$

Answer 2

$\tt\huge\purple{hello!!!}$

HERE IS UR ANSWER

$_____________________________$

$A=[3501]&B=[−4120]\\</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>★ To Find :-</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>⠀⠀⠀⠀⠀⠀\mapsto\large\bold\pink{A {}^{2} -2AB + B {}^{2} }↦A2−2AB+B2</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>★ Solution :-</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>\begin{gathered} \ \bold \red{For (1) } \mapsto\bold{A {}^{2} } \\ \\ \ \bold A {}^{2} =\left[\begin{array}{ccc}3 & 0 \\ 5 & 1 \end{array} \right] \left[\begin{array}{ccc}3 & 0 \\ 5 & 1 \end{array} \right] =\left[\begin{array}{ccc}9 + 0 & 0 + 0 \\ 15 + 5 & 5 + 1 \end{array} \right] =\left[\begin{array}{ccc}9 & 0 \\ 20 & 1 \end{array} \right] \\ \\ \bold \red{For (2) } \: \mapsto \bold{AB} \\ \\ \bold{AB = \left[\begin{array}{ccc}3 & 0 \\ 5 & 1 \end{array} \right]\left[\begin{array}{ccc}-4 & 2 \\ 1 & 0\end{array} \right] = \left[\begin{array}{ccc}-12 + 0 & 6 + 0 \\ - 20 + 1 & 10 + 0 \end{array} \right] =\left[\begin{array}{ccc}-12 & 6 \\ - 19 & 10 \end{array} \right] } \\ \\ \large \bold \red{For (3) } \mapsto \bold{B {}^{2} } \\ \\ \bold{B {}^{2} =\left[\begin{array}{ccc}-4 & 2 \\ 1 & 0 \end{array} \right] \left[\begin{array}{ccc}-4 & 2 \\ 1 & 0\end{array} \right] = \left[\begin{array}{ccc}-16 + 2 & - 8 + 0 \\ - 4 + 0 & 2 + 0 \end{array} \right] = \left[\begin{array}{ccc}18 & - 8 \\ - 4 & 2 \end{array} \right]}\end{gathered} For(1)↦A2 A2=[3501][3501]=[9+015+50+05+1]=[92001]For(2)↦ABAB=[3501][−4120]=[−12+0−20+16+010+0]=[−12−19610]For(3)↦B2B2=[−4120][−4120]=[−16+2−4+0−8+02+0]=[18−4−82]</p><p></p><p>⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀★ Therefore,⠀</p><p></p><p>⠀⠀⠀</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>\begin{gathered} \mapsto\large \bold \pink{A {}^{2} - 2 AB +B {}^{2} } = \bold{\left[\begin{array}{ccc}9 & 0 \\ 20 & 1 \end{array} \right] - 2}\left[\begin{array}{ccc} - 12 & 6 \\ - 19 & 10 \end{array} \right] + \left[\begin{array}{ccc}18 & - 8 \\ - 4 & 2 \end{array} \right] \\ \\ = \left[\begin{array}{ccc}9 & 0 \\ \large 20& 1 \end{array} \right] - \left[\begin{array}{ccc} - 24 & 12 \\ - 38 &20 \end{array} \right] + \left[\begin{array}{ccc}18 & - 8 \\ - 4 & 2 \\ \end{array} \right] \\ \\ \mapsto \large \bold\red{\left[\begin{array}{ccc}51 & - 20 \\ 54& - 17 \end{array} \right]}\end{gathered}↦A2−2AB+B2=[92001]−2[−12−19610]+[18−4−82]=[92001]−[−24−381220]+[18−4−82]↦[5154−20−17]</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>★ Hence,</p><p></p><p>⠀⠀⠀⠀⠀⠀</p><p></p><p>\begin{gathered} \rightarrow\large \bold \red{The Value = \pink{\left[\begin{array}{ccc}51 & - 20 \\ 54 & - 1 7\end{array} \right]}}\end{gathered}→TheValue=[5154</p><p></p><p>$