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Find 1/2(A+Aprime)and 1/2(A-Aprime), whe...

Find `1/2(A+Aprime)`and `1/2(A-Aprime)`, when `A=[[0,a, b],[-a,0,c],[-b,-c,0]]`

Text Solution

Verified by Experts

Given
`A=[[0,a, b],[-a,0,c],[-b,-c,0]]`
`A'=[[0,-a,-b],[a,0,-c],[b,c,0]]`
now
`1/2(A+A')=1/2([[0,a, b],[-a,0,c],[-b,-c,0]]+[[0,-a,-b],[a,0,-c],[b,c,0]])`
`1/2(A+A')=1/2[[0,0,0],[0,0,0],[0,0,0]]`= 0
and
`1/2(A-A')=1/2([[0,a, b],[-a,0,c],[-b,-c,0]]-[[0,-a,-b],[a,0,-c],[b,c,0]])`
`1/2(A-A')=1/2[[0,2a,2b],[-2a,0,2c],[-2b,-2c,0]]`
`1/2(A-A')=[[0,a,b],[-a,0,c],[-b,-c,0]]`= `A`
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