Question

Daoji and Drake are trying to find the determinant for the linear transformation T:R3 + R3 given by They proceed as follows: (a) Drake computes the length of T(@i), T(22) and T(3)and finds that all three are equal to 1. (b) Drake then says that because I does not change the lengths of the standard basis vectors, the volume of the image of the unit cube must be 1. (c) Drake then concludes that det(T) = 1. 17 (d) Daoji says that Drake must be wrong because T 1] = 0, and therefore the image of the unit cube must have zero volume. (e) Daoji says that even if the volume of the image of the unit cube is 1, this alone is not enough information to compute the determinant. Which of the following statements are true? Check all that apply. Drake made a mistake in step a Drake made a mistake in step b Drake made a mistake in step Daoji made a mistake in step d Daoji made a mistake in stepe

Answer 1

3-x os lol Length = / (+2) = 1 / 2 tangth: MessTas OD D-1 72 10-17 Leng Looo that) (+)? ✓ + + = : dongth: 18.12 (70) = 1 1 So brake donor made a mistakes in stp g. so option (a) is gaze, true. (6) The volum 'The volume of the image of the unit cube may not be 1. so brake made a mistake in step (6): () мој 6-ти determinant tablet . so brake made a mistake in steple). V2 so it has zeso vale me since nee I det (All det (All-voll so option (d) is true,

(e) from (d), (det (7)/- 10l (7) so, Davoji made a mistake in step te wird
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