MATH 1553 Midterm: MATH 1553 GT 11 17 Midterm a
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In this problem, if the statement is always true, circle t; otherwise, circle f. All matrices are assumed to have real entries: t, t, t, t, t. An upper-triangular matrix can have a complex (non-real) eigen- value. If an n n matrix a has a zero eigenvalue, then rank(a) < n. If a is an n n matrix and c is a scalar, then det(ca) = c det(a). 0 2 is similar to 2 0. 0 1 p 1, where p has columns v1 and v2. Given x v1 y x v2: with respect to the picture in (d), nd the b-coordinates of an eigenvector of. A with eigenvalue 1/2, where b = {v1, v2}. [5 points each: draw all eigenspaces of a, and label them with the corresponding eigenvalue: 0: compute an, where n 1 is any whole number. 2 2 matrix whose entries are formulas involving n.
