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HW5 - Math 3013 Homework Set 5 Problems from 2.1(pgs...

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Math 3013 Homework Set 5 Problems from § 2.1 (pgs. 134-136 of text): 1,3,11,12,13,16,23 Problems from § 2.2 (pgs. 140-141 of text): 1,3,5,7,11,12 Problems from § 2.3 (pgs. 152-154 of text): 1,2,3,4,5,7,13,15,19,29 Math 3013 Problem Set 5 Problems from § 2.1 (pgs. 134-136 of text): 1,3,11,12,13,16,23 Problems from § 2.2 (pgs. 140-141 of text): 1,3,5,7,11 Problems from § 2.3 (pgs. 152-154 of text): 1,2,3,4,5,7,13,15,19,29 1. (Problem 2.1.1 in text). Give a geometric criterion for a set of two distinct nonzero vectors in R 2 to be dependent. 2. (Problem 2.1.3 in text). Give a geometric criterion for a set of two distinct nonzero vectors in R 3 to be dependent. 3. (Problem 2.1.11 in text). Find a basis for the subspace spanned by the vectors [1 , 2 , 1 , 1], [2 , 1 , 0 , - 1], [ - 1 , 4 , 3 , 8], [0 , 3 , 2 , 5] R 4 . 4. (Problem 2.1.12 in text). Find a basis for the column space of the matrix A = 2 3 1 5 2 1 1 7 2 6 - 2 0 5. (Problem 2.1.13 in text). Find a basis for the row space of the matrix A = 1 3 5 7 2 0 4 2 3 2 8 7 6. (Problems 2.1.16 and 2.1.23 in text). Determine whether the following sets of vectors are dependent or independent. (a) { [1 , 3] , [ - 2 , - 6] } in R 2 . (b) { [1 , - 4 , 3] , [3 , - 11 , 2] , [1 , - 3 , - 4] } in R 3 . 7. (Problems 2.2.1, 2.2.3, and 2.2.5 in text). For each of the following matrices find the rank of the matrix, a basis for its row space, a basis for its column space, and a basis for its null space.
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