Question

Please solve this equation Given A = [ ⅛ ⅓ ], Evaluate A² - 4A​

Answer 1

$\large\underline\blue{\bold{Given \: Question :- }}$

$\bf \:If \: A = \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}, \: Find \: {A}^{2} - 4A$

$\large\underline\purple{\bold{Solution :- }}$

$\large \blue{\bf \:A = \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}}$

☆So,

$\large \blue{\bf \:  ⟼ {A}^{2} = A \times A}$

$\bf \:  ⟼ {A}^{2} = \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix} \times \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}$

$\bf \:  ⟼ {A}^{2} = \begin{bmatrix} 1 + 8 & 1 + 3\\ 8 + 24 & 8 + 9\end{bmatrix}$

$\bf \:  ⟼ {A}^{2} = \begin{bmatrix} 9 & 4\\ 32 & 17\end{bmatrix}$

☆To evaluate,

$\large \purple{\bf \: {A}^{2} - 4A }$

$\bf \:  ⟼ \begin{bmatrix} 9 & 4\\ 32 & 17\end{bmatrix} - 4\begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}$

$\bf \:  ⟼ \begin{bmatrix} 9 & 4\\ 32 & 17\end{bmatrix} - \begin{bmatrix} 4 & 4\\ 32 & 12\end{bmatrix}$

$\bf \:  ⟼ \begin{bmatrix} 9 - 4 & 4 - 4\\ 32 - 32 & 17 - 12\end{bmatrix}$

$\bf \:  ⟼ \begin{bmatrix} 5 & 0\\ 0 & 5\end{bmatrix}$

$\large{\boxed{\boxed{\bf{Hence, {A}^{2} - 4A = \begin{bmatrix} 5 & 0\\ 0 & 5\end{bmatrix} }}}}$

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Answer 2

GivenQuestion:−

\begin{gathered}\bf \:If \: A = \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}, \: Find \: {A}^{2} - 4A\end{gathered}IfA=[1813],FindA2−4A

\large\underline\purple{\bold{Solution :- }}Solution:−

\begin{gathered}\large \blue{\bf \:A = \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}}\end{gathered}A=[1813]

☆So,

\large \blue{\bf \:  ⟼ {A}^{2} = A \times A} ⟼A2=A×A

\begin{gathered}\bf \:  ⟼ {A}^{2} = \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix} \times \begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}\end{gathered} ⟼A2=[1813]×[1813]

\begin{gathered}\bf \:  ⟼ {A}^{2} = \begin{bmatrix} 1 + 8 & 1 + 3\\ 8 + 24 & 8 + 9\end{bmatrix}\end{gathered} ⟼A2=[1+88+241+38+9]

\begin{gathered}\bf \:  ⟼ {A}^{2} = \begin{bmatrix} 9 & 4\\ 32 & 17\end{bmatrix}\end{gathered} ⟼A2=[932417]

☆To evaluate,

\large \purple{\bf \: {A}^{2} - 4A }A2−4A

\begin{gathered}\bf \:  ⟼ \begin{bmatrix} 9 & 4\\ 32 & 17\end{bmatrix} - 4\begin{bmatrix} 1 & 1\\ 8 & 3\end{bmatrix}\end{gathered} ⟼[932417]−4[1813]

\begin{gathered}\bf \:  ⟼ \begin{bmatrix} 9 & 4\\ 32 & 17\end{bmatrix} - \begin{bmatrix} 4 & 4\\ 32 & 12\end{bmatrix}\end{gathered} ⟼[932417]−[432412]

\begin{gathered}\bf \:  ⟼ \begin{bmatrix} 9 - 4 & 4 - 4\\ 32 - 32 & 17 - 12\end{bmatrix}\end{gathered} ⟼[9−432−324−417−12]

\begin{gathered}\bf \:  ⟼ \begin{bmatrix} 5 & 0\\ 0 & 5\end{bmatrix}\end{gathered} ⟼[5005]

\begin{gathered}\large{\boxed{\boxed{\bf{Hence, {A}^{2} - 4A = \begin{bmatrix} 5 & 0\\ 0 & 5\end{bmatrix} }}}}\end{gathered}Hence,A2−4A=[5005]

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