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For the matrix A={bmatrix} 1 & 5 6 & 7 {bmatrix}, verify tha

Question

For the matrix $A = [1657]$ , verify that
(i) $(A + A^{'})$ is a symmetric matrix
(ii) $(A - A^{'})$ is a skew symmetric matrix.

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Charlotte Discussed

For the matrix

A = [1657]

, verify that
(i)

(A + A^{'})

is a symmetric matrix
(ii)

(A - A^{'})

is a skew symmetric matrix.

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Text solutionVerified

A^{'} = [1567]

(i)

A + A^{'} = [1657] + [1567] = [2111114]

∴ (A + A^{'})^{'} = [2111114] = A + A^{'}

Hence,

(A + A^{'})

is a symmetric matrix.

(ii)

A - A^{'} = [1657] - [1567] = [01 - 1 0]

∴ (A - A^{'})^{'} = [01 - 1 0] = - [01 - 1 0] = - (A - A^{'})

Hence,

(A - A^{'})

is a skew symmetric matrix.

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Question Text	For the matrix $A = [1657]$ , verify that (i) $(A + A^{'})$ is a symmetric matrix (ii) $(A - A^{'})$ is a skew symmetric matrix.
Answer Type	Text solution:1
Upvotes	150