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(i) Show that the matrix A=[[1,-1, 5],[-...

(i) Show that the matrix `A=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]]`is a symmetric matrix. (ii) Show that the matrix `A=[[0, 1,-1],[-1, 2, 1],[ 1,-1, 0]]`is a skew symmetric matrix.

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(i) Given `A=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]]`
`therefore`
`A'=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]]`
Since `A'=A`
Hence, A is a symmetric matrix.

(ii) Given `A=[[0, 1,-1],[-1, 0, 1],[ 1,-1, 0]]`
`therefore` `A'=[[0, -1,1],[1, 0, -1],[-1,1, 0]]=- [[0, 1,-1],[-1, 0, 1],[ 1,-1, 0]]`
`A'=-A`
Hence, A is a skew-symmetric matrix.
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