Question

If A is a matrix (5 x y 0 ) and A=transpose of A then find x + y
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Answer 1

SOLUTION

GIVEN

$\displaystyle A= \begin{pmatrix} 5 & x\\ y & 0 \end{pmatrix}$

A = transpose of A

TO DETERMINE

The value of x + y

EVALUATION

Here the given matrix is

$\displaystyle A= \begin{pmatrix} 5 & x\\ y & 0 \end{pmatrix}$

Now

transpose of A

$\displaystyle = {A }^{t}$

$\displaystyle = \begin{pmatrix} 5 & y\\ x & 0 \end{pmatrix}$

By the given condition

$\displaystyle \begin{pmatrix} 5 & x\\ y & 0 \end{pmatrix} = \displaystyle \begin{pmatrix} 5 & y\\ x & 0 \end{pmatrix}$

Comparing both sides we get x = y

Hence the required value of x + y

= y + y

= 2y

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