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)]

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Answer :(i) `A=[(3,3),(3,-1)]+[(0,2),(-2,0)]`
(II) `A=[(6,-2,2),(-2,3,-1),(2,-1,3)]+[(0,0,0),(0,0,0),(0,0,0)]`
(III) `A=[(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)A=[(1,2),(2,2)]+[(0,3),(-3,0)]`


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