Mathematics · Linear Algebra

Let v &in; &reals; 3 be a non-zero vector. Define a linear transformation T : &reals; 3 → &reals; 3 by T(x) = x - 2(x · v) v · v v, where x · y denotes the standard inner product in &reals; 3 . Which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

The determinant of T is -1

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Let v &in; &reals; 3 be a non-zero vector. Define a linear transformation T : &reals; 3 &rarr; &reals; 3 by T(x) = x - 2(x &middot; v) v &middot; v v, where x &middot; y denotes the standard inner product in &reals; 3 . Which of the following statements is true?