Question

if A=[ 4 x+2] is a symmetric
[ 2x-3 x+1 ]
matrix then find value of x.​

Answer 1

Answer:

For a matrix 'A' to be symmetric in nature, the condition to be satisfied is:

• A = A'

where, A' refers to the Transpose of the Matrix 'A'.

According to the question, the given matrix is a symmetric matrix. We are required to calculate the value of 'x' based on the given conditions.

Given Matrix:

$\left[\begin{array}{ccc}4&(x+2)\\(2x-3)&(x+1)\end{array}\right]$

Calculating the transpose of the above matrix we get:

$\left[\begin{array}{ccc}4&(2x-3)\\(x+2)&(x+1)\end{array}\right]$

Since it is a symmetric matrix, the corresponding elements are equal. Hence, on comparing a₂₁ from both matrices, we get:

⇒ (x + 2) = (2x - 3)

⇒ 2 + 3 = 2x - x

⇒ 5 = x

Hence the required value of 'x' is 5 for which the given matrix is symmetric.