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Unformatted text preview: MATH 340; EXAM # 1, 100 points, November 13 , 2007 (R.A.Brualdi) TOTAL SCORE : Name: These R. Solutions I. (42 points; 3 points each) Answer the following questions as True (T) or False (F) by circling T or F below (no justification wanted): 1. T If u 1 ,u 2 ,u 3 ,u 4 ,u 5 are linearly independent vectors in a 5-dimensional subspace U of R 8 , then they are a basis of U . 2. T If v 1 ,v 2 ,v 3 ,v 4 ,v 5 spans a 5-dimensional subspace V of R 8 , then they are a basis of V . 3. T If A is a 6 by 8 matrix then you can be sure that the homogeneous system Ax = 0 has a non-trivial solution. 4. T A linearly independent set of 3 vectors in 5-dimensional vector space V can always be enlarged to a basis of V . 5. F A set of 8 vectors in a 6-dimensional vector space U always contains 6 vectors that form a basis of U . 6. F The set of all singular 4 by 4 matrices is a subspace of the vector space M 4 , 4 of all 4 by 4 matrices. 7. F A 3 by 5 matrix A could have rank 4. 1 8. F The set of all vectors [ a b c ] in R 3 with a + b + c 0 forms a subspace of R 3 ....
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