If A = 2 - 3 - 4 1 , then A T 2 + 12 A T =

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Question: Answered & Verified by Expert

If

A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]

, then

{(A^{T})}^{2} + {(12 A)}^{T} =

MathematicsMatricesAP EAMCETAP EAMCET 2022 (04 Jul Shift 2)

Options:

A $5 [\begin{matrix} 8 & 12 \\ - 9 & 5 \end{matrix}]$
B $5 [\begin{matrix} 8 & - 9 \\ - 12 & 5 \end{matrix}]$
C $[\begin{matrix} 40 & - 45 \\ 60 & 25 \end{matrix}]$
D $[\begin{matrix} 40 & - 60 \\ - 45 & 25 \end{matrix}]$

Solution:

1034 Upvotes Verified Answer

The correct answer is:

[\begin{matrix} 40 & - 60 \\ - 45 & 25 \end{matrix}]

Given:
$A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$
$\Rightarrow A^{T} = [\begin{matrix} 2 & - 4 \\ - 3 & 1 \end{matrix}]$
$\Rightarrow {(A^{T})}^{2} = [\begin{matrix} 2 & - 4 \\ - 3 & 1 \end{matrix}] [\begin{matrix} 2 & - 4 \\ - 3 & 1 \end{matrix}]$
$\Rightarrow {(A^{T})}^{2} = [\begin{matrix} 16 & - 12 \\ - 9 & 13 \end{matrix}]$
And,
$12 A = [\begin{matrix} 24 & - 36 \\ - 48 & 12 \end{matrix}]$
$\Rightarrow {(12 A)}^{T} = [\begin{matrix} 24 & - 48 \\ - 36 & 12 \end{matrix}]$
So,
${(A^{T})}^{2} + {(12 A)}^{T} = [\begin{matrix} 16 & - 12 \\ - 9 & 13 \end{matrix}] + [\begin{matrix} 24 & - 48 \\ - 36 & 12 \end{matrix}]$
$\Rightarrow {(A^{T})}^{2} + {(12 A)}^{T} = [\begin{matrix} 40 & - 60 \\ - 45 & 25 \end{matrix}]$

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