Exam1_Fall_2013_mod

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Name ______________________________ Examination 1 M340L-CS 1. Use extra paper to determine your solutions then neatly transcribe them onto these sheets. 2. Do not submit the scratch sheets. However, all of the work necessary to obtain the solution should be on these sheets. 3. Comment on all errors and omissions and enclose the 1. [20] Mark T(rue) or F(alse) for each of the following statements: ____a. A consistent system of linear equations could have no solution. ____b. The column space of A is the set of all vectors that can be written as Ax for some x . ____c. The solution set of the linear system whose augmented matrix is 1 2 3 a a a b is the same as the solution set of the equation 1 1 2 2 3 3 . x x x a a a b ____d. When u and v are nonzero vectors, Span { u, v } contains only the line through u and the origin, and the line through v and the origin. ____e. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.

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