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If A={:[(5,6),(7,8)]:}," then "(A+A^(T))...

If `A={:[(5,6),(7,8)]:}," then "(A+A^(T))/(2)` is _______ .

A

symmetric

B

skew symmetric

C

diagonal

D

unit matrix

Text Solution

Verified by Experts

The correct Answer is:
A
`A={:[(5,6),(7,8)]:},A^(T)={:[(5,7),(6,8)]:}`
`A+A^(T)={:[(5+5,6+7),(7+6,8+8)]:}`
`A+A^(T)={:[(10,13),(13,16)]:}`
`(1)/(2)(A+A^(T))={:[((10)/(2),(13)/(2)),((13)/(2),(16)/(2))]:}={:[(5,(13)/(2)),((13)/(2),8)]:}`
`(1)/(2)[(A+A^(T))]^(T)=(1)/(2)[A+A^(T)]`
`:." It is symmetric".`
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