Question

Determine if the linear transformation is (a) one-to-one, (b) onto. T(x1,x2,x3)=(2x1 −4x2,x1 −x3,−x2 +3x3).

Determine if the linear transformation is (a) one-to-one, (b) onto.

T(x1,x2,x3)=(2x1 −4x2,x1 −x3,−x2 +3x3).

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Answer #1

Please find the uploaded files for the answer. If you still have some doubts, you can comment below. I solved this question using 2 methods.

Method 1: Use Rank-Nullity Theorem.

Method 2: (Basic approach)Use definitions of One-one and onto a map.

Please rate the answer. Thanking you.

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