M-221 Midterm: Montana State MATH 221 Exam3
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Show proper work for full credit in problems 3-6: (2pts each) answer true or false. If the row vectors of a are linearly independent, then a is an invertible matrix. (b) 2 form a basis for r3 . (c) If a is an m n matrix with nullity(a) = 0, then col(at ) = rn . (d) Every subspace of dimension 2 in r4 is represented by a plane that goes through the origin. (e) , ~vn} rn, then the set {~v1, ~v2, . , ~vn} is a basis for w . (f) If a is a 4 3 matrix, then the row vectors of a must be linearly dependent: (2pt each) short answer. Give the following: (i) the size of a is (ii) rank(a) = (iii) nullity(a) = (iv) rank(at ) = (v) nullity(at ) : (8pts) let a~x = ~b be a linear system of m equations in n unknowns.
