MTH 125 Study Guide - Midterm Guide: Diagonalizable Matrix, Linear Independence, Cross Product
12 Oct 2018
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Part a - true/false questions for each of the following assertions, answer t (= true) if and only if the assertion is always true. Carefully print the letter of the answer you think is most correct in the box at the top of page 2. Each right answer earns 2 points and each wrong answer earns 0 points. 1. (a) carefully de ne the concepts of eigenvalue and eigenvector. [5 points] (b) for the remainder of this question let b = Find the characteristic polynomial of b in factored form and the eigenvalues of b. Question 1 continued. (c) find an eigenvector corresponding to the smallest eigenvalue of b and nd its eigenspace. [6 points] (d) state a theorem that justi es why b is diagonalizable and state a diagonal matrix that. 2. (a) carefully de ne what it means for the cross product to be (i) anti-commutative.
