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):}]

Express the following matrices as the sum of a symmetric and a skew sy

1.	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):}]
Answer» Answer :(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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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):}]

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