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Express the following matrices as the su...

Express the following matrices as the sum of a symmetric and a skew symmetric matrix :
(i) `[{:(3,5),(1,-1):}]` (ii) `[{:(6,-2,2),(-2,3,-1),(2,-1,3):}]` (iii) `[{:(3,3,-1),(-2,-2,1),(-4,-5,2):}]` (iv) `[{:(1,5),(-1,2):}]`

Text Solution

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The correct Answer is:
(i) `thereforeA=[{:(3,3),(3,-1):}]+[{:(0,2),(-2,0):}]`
(ii) `=[{:(6,-2,2),(-2,3,-1),(2,-1,3):}]+[{:(0,0,0),(0,0,0),(0,0,0):}]`
(iii) `=[{:(3,(1)/(2),-(5)/(2)),((1)/(2),-2,-2),(-(5)/(2),-2,2):}]+[{:(0,(5)/(2),(3)/(2)),(-(5)/(2),0,3),(-(3)/(2),-3,0):}]`
(iv) `=[{:(1,2),(2,2):}]+[{:(0,3),(-3,0):}]`
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