Q1. (a) Distinguish between Singular and Non-singular transformation on vector spaces. (b) Define T from R3 R3 by T (X1, ,X2, X3) = (2X1 + X2, X2 + x3 - X1,3X, + X2 + x3
transformation.

Q2. (a) Define a linear operator R3 by T(x, y, z) = (3x + z , -2x + y; -x + 2y + 4z)
Compute the matrix T in the basis {e1 = (1,2,0), e2 = (1,0,1), e3 = (-1,2,1)}
And show that [T]e[V]e = [T](V)e where V = (4, -7,5)

(b) What do you understand by the term "Homomorphism?"
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