M-221 Quiz: Montana State MATH 221 quiz1key
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Show proper work for full credit in problems 2-9: (2pts each) answer true or false. No justi cation required . (a) (b) (c) (d) (e) (f) If the vectors ~u and ~v are not orthogonal, then the set {~u, ~v} is linearly dependent. Given any matrix a, the matrices aat and at a are symmetric. Every system of linear equations has a solution. If a is an m n matrix with nullity(a) = 0, then col(a) = rm . If an n n matrix a is diagonalizable, then a must have n distinct eigenvalues. If a is a symmetric matrix, then a is hermitian: (20pts) prove that: (a) if a is a hermitian matrix, then a is normal. Proof: (b) if a real-valued n n matrix a is orthogonally diagonalizable, then a is symmetric. That is, show that ~vi ~vj for i 6= j. T (f) (6pts) find a unitary matrix q (i. e. q = q.
