MATH 121A Midterm: SampleMidterm1
Document Summary
Prove that if {x, y} is a basis for v , then so is {x + y, 2iy}: let v be an r-vector space. Prove that if the set of vectors {u, v} is linearly dependent, then one of the vectors is a scalar multiple of the other: true/false: the span of a set of k vectors {v1, v2, . Prove your answer: consider c2 as a complex vector space, and consider the subset {(x, y) 2 c2 | real(x) = real(y)}. Prove or disprove: carefully de ne the following terms. Range: not enough details: the set of vectors in the image of t , enough details: let v, w denote two vector spaces over a eld f , and let t : v ! The range of t , denoted r(t ), is.
