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Exam1_Fall_2013_mod

# The solution set of the linear system whose augmented

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Unformatted text preview: e solution set of the linear system whose augmented matrix is a1 a2 a3 b is the same as the solution set of the equation x 1a1 x 2 a2 x 3a3 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. ____f. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. ____g. The equation x = p + tv describes a line through v parallel to p. ____h. The columns of a matrix A are linearly independent if the equation Ax = 0 has the trivial solution. 2 . F ind...
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