For the matrix, verify that

(i) is a symmetric matrix

(ii) is a skew symmetric matrix

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Solution

(i)

Hence, is a symmetric matrix.

(ii)

Hence, is a skew-symmetric matrix.

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Similar questions

Q. For the matrix

A = [\begin{matrix} 1 & 5 6 & 7 \end{matrix}]

, verify that
(i)

(A + A^{'})

is a symmetric matrix
(ii)

(A - A^{'})

is a skew symmetric matrix.

For the matrix, $A = [\begin{matrix} 1 & 5 6 & 7 \end{matrix}]$ , verify that

(i) (A+A') is a symmetric matrix.

(ii) (A-A') is a skew-symmetric matrix.

Q. For the matrix , verify that (i) is a symmetric matrix (ii) is a skew symmetric matrix

(i) Show that the matrix is a symmetric matrix

(ii) Show that the matrix is a skew symmetric matrix

Q. (i) Show that the matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 5 \end{matrix} \begin{matrix} - 1 21 \end{matrix} \begin{matrix} 513 \end{matrix} ⎤ ⎥ ⎦

is a symmetric matrix

(ii) Show that the matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 0 - 1 1 \end{matrix} \begin{matrix} 10 - 1 \end{matrix} \begin{matrix} - 1 10 \end{matrix} ⎤ ⎥ ⎦

is a skew symmetric matrix.

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For the matrix, verify that (i) is a symmetric matrix (ii) is a skew symmetric matrix

(i) Hence, is a symmetric matrix. (ii) Hence, is a skew-symmetric matrix.

For the matrix, verify that

(i) is a symmetric matrix

(ii) is a skew symmetric matrix

(i)

Hence, is a symmetric matrix.

(ii)

Hence, is a skew-symmetric matrix.