## Question

###### In each item write down the representing matrix of the given linear transformation T : R: + R: with respect to the standard basis of RS, {(1,0,0), (0,1,0) , (0,0,1)}. (a) T(a,b,c) = (a _ b+c,-2a _ b+ 3c,a + 4c).T is such that (1,0,1) and (0,1,1) are eigenvectors of eigenvalue 2 and T(0,0,1) (1,1,1).T(1,0,1) = (,2,0) and a basis of ker(T) is {(0,2,1), (-1,1,0)}.

In each item write down the representing matrix of the given linear transformation T : R: + R: with respect to the standard basis of RS, {(1,0,0), (0,1,0) , (0,0,1)}. (a) T(a,b,c) = (a _ b+c,-2a _ b+ 3c,a + 4c). T is such that (1,0,1) and (0,1,1) are eigenvectors of eigenvalue 2 and T(0,0,1) (1,1,1). T(1,0,1) = (,2,0) and a basis of ker(T) is {(0,2,1), (-1,1,0)}.

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