Kunze Linear Algebra · Problem 3.2.3

Linear Transformations

Mathematics — Methods · invertibility-linear-operator-r3

Problem

Let TT be the linear operator on R3R^3 defined by T(x1,x2,x3)=(3x1,  x1−x2,  2x1+x2+x3).T(x_1, x_2, x_3) = (3x_1,\; x_1 - x_2,\; 2x_1 + x_2 + x_3). Is TT invertible? If so, find a rule for T−1T^{-1} like the one which defines TT.

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