For the matrix- A - begin bmatrix 185 16 - 7 1endbmatrix - verify that A-A-is a skew-symmetric matrix-

A A'=[ 1 amp; 5; 6 amp; 7; ]'=[ 1 amp; 5; 6 amp; 7; ] [ 1 amp; 6; 5 amp; 7; ]=[ 0 amp; 1; 1 amp ...

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Standard XII

Mathematics

Transpose of a Matrix

For the matri...

Question

For the matrix, $A = [\begin{matrix} 1 & 5 6 & 7 \end{matrix}]$ , verify that
(A-A')is a skew-symmetric matrix.

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Solution

$A - A^{'} = {[\begin{matrix} 1 & 5 6 & 7 \end{matrix}]}^{'} = [\begin{matrix} 1 & 5 6 & 7 \end{matrix}] - [\begin{matrix} 1 & 6 5 & 7 \end{matrix}] = [\begin{matrix} 0 & - 1 1 & 0 \end{matrix}] \Rightarrow A - A^{'} = [\begin{matrix} 0 & - 1 1 & 0 \end{matrix}] a n d (A - A^{'})^{'} = [\begin{matrix} 0 & 1 - 1 & 0 \end{matrix}] = - [\begin{matrix} 0 & - 1 1 & 0 \end{matrix}] = (A - A^{'})$
$[∵ A^{'} = - A$ , then A is a skew -symmetric matrix]
Hence, (A-A')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

Show that the matrix, $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & - 1 - 1 & 0 & 1 1 & - 1 & 0 \end{matrix} ⎤ ⎥ ⎦$ is a skew -symmetric matrix.

For the matrix, verify that

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For the matrix, A=[1567], verify that (A-A')is a skew-symmetric matrix.

A−A′=[1567]′=[1567]−[1657]=[0−110]⇒A−A′=[0−110]and(A−A′)′=[01−10]=−[0−110]=(A−A′) [∵A′=−A, then A is a skew -symmetric matrix] Hence, (A-A')is a skew -symmetric matrix.

For the matrix, $A = [\begin{matrix} 1 & 5 6 & 7 \end{matrix}]$ , verify that
(A-A')is a skew-symmetric matrix.