MATH 515 Midterm: Kansas State MATH 515 515t2s03
7 Mar 2019
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Show all work for full credit: find the inverse of the matrix matrix. By row reducing an augmented: find the determinant of the matrix. 1 1(cid:19) as a product of elementary matrices. 2: let a mn n(f ) and b mn n(f ) be two square n n matrices. Prove that both a and b are invertible: let: t : v w be a linear transformation of vector spaces over a eld f . Assume that both v and w are nite dimensional. Let b1 and b2 be two bases for v , and let b3 and b4 be two bases for w . B2 be the matrices of the linear transformation t with respect to the various bases. Prove that rank(m ) = rank(n ): let v be a nite dimensional vector space over a eld f . Let f : v f and g : v f be two linear functionals.
