Question: Decide whether the following maps T : IR3 7? IR3 are linear. If they are linear, find a matrix A such that T(x) = Ax.

Decide whether the following maps T : IR3 7? IR3 are linear. If they are linear, find a matrix A such that T(x) = Ax. If they are not linear, explain why. (i) T ? ? x1 x2 x3 ? ? = ? ? x 2 1 1 0 ? ? (ii) T ? ? x1 x2 x3 ? ? = ? ? 0 x2 ?x2 ? ? (iii) T ? ? x1 x2 x3 ? ? = ? ? x3 0 x1 + x2 ?

1. Decide whether the following maps T : IR3 -> R3 are linear. If they are linear, find a matrix A such that T(x) = Ax. If they are not linear, explain why. (i) T I2 I1 (ii) T = (iii) T = 0 1 + 12

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