MATH 1553 Quiz: MATH 1553 GT 11 10 Quiz b
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[5 points] write a mathematically correct de nition of an eigenvalue. Is an eigenvalue of an n n matrix a provided that there exists a nonzero solution v to the equation av = v. [4 points] consider the matrix a for the transformation that re ects over a line l. Find all eigenvalues of a, and draw a picture of an eigenvector for each eigenvalue in the box below. The only vectors that are taken to a scalar multiple are the vectors on l, which are not moved, and the vectors perpendicular to l, which are negated. The former have eigenvalue 1, and the latter have eigenvalue 1. The roots are f ( ) = 2 tr(a) + det(a) = 2 3 1.
