A=4x+22x-3x+1 is symmetric, then x - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$3$
B
$5$
C
$2$
D
$4$

Solution:

Given , $A = [\begin{matrix} 4 & x + 2 \\ 2 x - 3 & x + 1 \end{matrix}]$ is symmetric

A matrix , $A$ is symmetric if $A = A^{T}$

Hence

$A^{T} = [\begin{matrix} 4 & 2 x - 3 \\ x + 2 & x + 1 \end{matrix}] \Rightarrow A = A^{T} [\begin{matrix} 4 & x + 2 \\ 2 x - 3 & x + 1 \end{matrix}] = [\begin{matrix} 4 & 2 x - 3 \\ x + 2 & x + 1 \end{matrix}]$

Equating the corresponding elements

$\Rightarrow x + 2 = 2 x - 3 \Rightarrow 2 + 3 = 2 x - x \Rightarrow x = 5$

$A = [\begin{matrix} 4 & x + 2 \\ 2 x - 3 & x + 1 \end{matrix}]$ is symmetric, then $x$

Solution:

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