MATH 1553 Midterm: MATH 1553 GT 10 20 Midterm c Solution
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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. , vn} spans r4, then n = 4. If m > n and t (x) = ax, then t is not onto. If a has a pivot in every row, then nul a = {0}. There exists a 7 4 matrix a such that dim nul a = 5. You can only conclude n 4: true, true. The null space is {0} if a has a pivot in every column: false. The null space is a subspace of r4, hence cannot be 5-dimensional. Short answer questions: you need not explain your answers.
