MATH 1553 Midterm: MATH 1553 GT 10 20 Midterm a
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Please read all instructions carefully before beginning: each problem is worth 10 points. In the following problems, a is an m n matrix (m rows, n columns). Circle t if the statement is always true, and circle f otherwise. You do not need to explain your answer: t, t, t, t, t. If a has a pivot in every column, then nul a = {0}. If m > n and t (x) = ax, then t is not one-to-one. A translate of a span is a subspace. There exists a 4 7 matrix a such that dim nul a = 5. , vn} is a basis for r4, then n = 4. Short answer questions: you need not explain your answers. 1 1 : write a nonzero vector in col a, where a = 1 1. , vm} is linearly dependent if: which of the following are onto transformations? (check all that apply. )
