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(i) Show that the matrix A=[ {matrix} 1 -1 5 {matrix}{matri

Question

(i) Show that the matrix $A = ⎣ ⎡ 1 - 1 5 - 1 21 513 ⎦ ⎤$ is a symmetric matrix

(ii) Show that the matrix $A = ⎣ ⎡ 0 - 1 1 10 - 1 - 1 10 ⎦ ⎤$ is a skew symmetric matrix.

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(i) Show that the matrix

A = ⎣ ⎡ 1 - 1 5 - 1 21 513 ⎦ ⎤

is a symmetric matrix

(ii) Show that the matrix

A = ⎣ ⎡ 0 - 1 1 10 - 1 - 1 10 ⎦ ⎤

is a skew symmetric matrix.

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Text solutionVerified

(i) We have :

A^{'} = ⎣ ⎡ 1 - 1 5 - 1 21 513 ⎦ ⎤ = A

∴ A^{'} = A

Hence,

A

is a Symmetric matrix.

(ii) We have:

A^{'} = ⎣ ⎡ 0 - 1 1 10 - 1 - 1 10 ⎦ ⎤ = - ⎣ ⎡ 0 - 1 1 10 - 1 - 1 10 ⎦ ⎤ = - A

∴ A^{'} = - A

Hence,

A

is a skew symmetric matrix.

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Question Text	(i) Show that the matrix $A = ⎣ ⎡ 1 - 1 5 - 1 21 513 ⎦ ⎤$ is a symmetric matrix (ii) Show that the matrix $A = ⎣ ⎡ 0 - 1 1 10 - 1 - 1 10 ⎦ ⎤$ is a skew symmetric matrix.
Answer Type	Text solution:1
Upvotes	150