Question

For any square matrix a with a real number prove that a+a' is a symmetry

Answer 1

Answer:

See attachment

Step-by-step explanation:

Answer 2

For any square matrix a with a real number, a+a' is a symmetry

Given,

Matrix a is a square matrix

To Find,

Prove that for any square matrix a with a real number a+a' is a symmetry

Solution,

According to the question, matrix a is a square matrix.

Then, let a be a square matrix of order n

For symmetry matrix:

Let X= a+a' ___________(1)

and now we transpose both sides, we get

X'= ( a+a')'

or, X'= a'+ (a')'

or, X'= a' + a [ We know that, (a')' =a]

or, X'= a+ a' ___________(2)

From equation (1) and (2) we find, X=X'

So, a+a' is a symmetry.

Hence, For any square matrix a with a real number, a+a' is a symmetry [ Proved]

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