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

Correct answer: (D) 40 -60 -45 25. Given: A= 2 -3 -4 1 ⇒A^T= 2 -4 -3 1 ⇒AT^2= 2 -4 -3 1 2 -4 -3 1 ⇒AT^2= 16 -12 -9 13 And, 12A= 24 -36 -48 12 ⇒12A^T= 24 -48 -36 12 So, AT^2+12A^T= 16 -12 -9 13 + 24 -48 -36 12 ⇒AT^2+12A^T= 40 -60 -45 25

Q43 / 160 · AP EAMCET 2022 (04 Jul Shift 2) · Mathematics

If $A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$ , then ${(A^{T})}^{2} + {(12 A)}^{T} =$

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

Solution

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

Hence, the correct answer is option: 'D'.

If A=2-3-41, then AT2+12AT=

Solution

Relevant Questions

If $A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]$ , then ${(A^{T})}^{2} + {(12 A)}^{T} =$