show that a matrix which is both symmetric and skew symmetric is a zero matrix.
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Hy mate
Toolbox:A square matrix A=[aij] is said to be symmetric if A'=A that is [aij]=[aji] for all possible value of i and j.A square matrix A=[aij] is said to be skew symmetric if A'=-A that is [aij]=−[aji] for all possible value of i and j.
Step 1: If a matrix is both symmetric and skew symmetric matrix ,then
A is symmetric matrix
⇒aij=aji
A is a skew symmetric matrix
⇒aij=−aji
Step 2: If aij=aji=−aji
⇒aij=0
Hence A is a zero matrix.
so (B) is the correct answer.
I hope it will help you
thank you ❤
Toolbox:A square matrix A=[aij] is said to be symmetric if A'=A that is [aij]=[aji] for all possible value of i and j.A square matrix A=[aij] is said to be skew symmetric if A'=-A that is [aij]=−[aji] for all possible value of i and j.
Step 1: If a matrix is both symmetric and skew symmetric matrix ,then
A is symmetric matrix
⇒aij=aji
A is a skew symmetric matrix
⇒aij=−aji
Step 2: If aij=aji=−aji
⇒aij=0
Hence A is a zero matrix.
so (B) is the correct answer.
I hope it will help you
thank you ❤
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I think it will help u
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