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Maths-

General

Easy

Question

If $A equals open square brackets table row 4 cell x plus 2 end cell row cell 2 x minus 3 end cell cell x plus 1 end cell end table close square brackets$ is symmetric then trace of A is

5
-10
10
15

hint Hint:

A square matrix B which of size n × n is considered to be symmetric if and only if B^T = B. Consider the given matrix B, that is, a square matrix that is equal to the transposed form of that matrix, called a symmetric matrix.
This can be represented as: If B = ${[b_{i j}]}_{n \times n}$ is the symmetric matrix, then $b_{i j}$ = $b_{j i}$ for all i and j or 1 ≤ i ≤ n, and 1 ≤ j ≤ n. Here,

n is any natural number.

$b_{i j}$ is an element at position (i, j) which is i^th row and j^thcolumn in matrix B and

$b_{j i}$ is an element at position (j, i) which is j^th row and i^th column in matrix B.

The correct answer is: 10

Given $A equals open square brackets table row 4 cell x plus 2 end cell row cell 2 x minus 3 end cell cell x plus 1 end cell end table close square brackets$ is symmetric.
$A to the power of T space equals space A T r a n s p o s e space i s space i n t e r c h a n g i n g space o f space r o w s space a n d space c o l u m n s space i n space a space m a t r i x. rightwards double arrow open square brackets table row 4 cell 2 x space minus space 3 end cell row cell x space plus space 2 end cell cell x space plus space 1 end cell end table close square brackets space equals space open square brackets table row 4 cell x space plus space 2 end cell row cell 2 x space minus space 3 end cell cell x space plus space 1 end cell end table close square brackets E q u a t i n g rightwards double arrow space x plus space 2 space equals space 2 x space minus space 3 rightwards double arrow x space space equals space 5 T h e r e f o r e space A space equals space open square brackets table row 4 cell 5 space plus space 2 end cell row cell 2 left parenthesis 5 right parenthesis space minus space 3 end cell cell 5 space plus space 1 end cell end table close square brackets space equals space open square brackets table row 4 7 row 7 6 end table close square brackets T r left parenthesis A right parenthesis space equals space I n space a space comma m a t r i x space s u m space o f space p r i n c i p a l space d i a g o n a l space e l e m e n t s space i s space c a l l e d space a s space t r a c e T r left parenthesis A right parenthesis space equals space 4 space plus space 6 space equals space 10$
Thus, trace of A is 10.

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