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Question
(i) Show that the matrix A=⎡⎢⎣1−15−121513⎤⎥⎦ is a symmetric matrix
(ii) Show that the matrix A=⎡⎢⎣0−1110−1−110⎤⎥⎦ is a skew symmetric matrix.
(ii) Show that the matrix A=⎡⎢⎣0−1110−1−110⎤⎥⎦ is a skew symmetric matrix.
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Solution
(i) We have :
A′=⎡⎢⎣1−15−121513⎤⎥⎦=A
∴A′=A
Hence, A is a Symmetric matrix.
(ii) We have:
A′=⎡⎢⎣0−1110−1−110⎤⎥⎦=−⎡⎢⎣0−1110−1−110⎤⎥⎦=−A
∴A′=−A
Hence, A is a skew symmetric matrix.
A′=⎡⎢⎣1−15−121513⎤⎥⎦=A
∴A′=A
Hence, A is a Symmetric matrix.
(ii) We have:
A′=⎡⎢⎣0−1110−1−110⎤⎥⎦=−⎡⎢⎣0−1110−1−110⎤⎥⎦=−A
∴A′=−A
Hence, A is a skew symmetric matrix.
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is
a symmetric matrix
is
a skew symmetric matrix