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Example 0.1. Determine if the linear transformation T: R3 R3 defined by T(x) = 11 2 0 1 3 -1 2 x L 2011 is invertible. Additi
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Example o Soluhion 2. Denote A = -1 2. T R3 by Tox) A x det(A) ) - 2 (La) ( 3-4) +o --2 (-1) = -1+2 = | .det CA) = 1 ±0 . matTx Tx Ty then T is one-One. is onto : show To Let A exist x A e R T(A)A (ABY)A (A )- (A A)y T(x) T (x) y T(x)=4 FoY euery e

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