a) image b) kernel c) Identity d) Null 9) If T: V → W be a linear operator and S is a finite basis of V then _.
a) Identity b) nonidentity c) Linear transformation d) Invertible 6) If F & G is linear then G∘ F is also _ a) Non- linear b) Inverse c) Linear d) Transfer 7) If dim(V W) = dim Mm x n(R) = _ a) m n b) dim V dim W c) both (1) & (2) d) 0 8) The _ of T is the set of elements in V that maps into the zero vector 0 ∈ W. a) n2 b) A c) n d) R 2) If T is a linear transformation then which of the following is true ? a) T(0) = x b) T(x) = - T(x) c) T(0) = 0 d) T(k x) = k + T(x) 3) A linear transformation T : V → W is invertible then it is a _ a) inverse b) Linearly independent c) Isomorphism d) Dependent 4) If T: R2→ R2 is a linear transformation defined by T(1, 0) = (2, 3, 1) and T(1, 1) = (3, 0, 2) then which of the following is correct ? a) T(x, y) = ( x + y, 2 x + y, 3 x – 3 y) b) T(x, y) = (2 x + y, 3 x – 3 y, x + y) c) T(x, y) = (2 x – y, 3 x + 3 y, x – y) d) T(x, y) = (x – y, 2 x – y, 3 x + 3 y) 5) A function T : V → W is called _ if T(x) = x ∀ x ∈ V. 1) If A: Rn→ Rn is a linear transformation given by n x n matrix then it is isomorphic if and only if Rank (A) = _.
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