HW2 - 3. (Problems 1.4.13 and 1.4.15 in text). Find all...

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Math 3013 Homework Set 2 Problems from § 1.4 (pg. 68-69 of text): 1,3,5,9,12,13,15,25 1. (Problems 1.4.1, 1.4.3, and 1.4.5 in text). Reduce the following matrices to row-echelon form, and reduced row-echelon form. (a) 2 1 4 1 3 2 3 - 1 6 (b) 0 2 - 1 3 - 1 1 2 0 1 1 - 3 3 1 5 5 9 (c) - 1 3 0 1 4 1 - 3 0 0 - 1 2 - 6 2 4 0 0 0 1 3 - 4 2. (Problems 1.4.9 and 1.4.12 in text). Describe all the solutions of a linear system whose corresponding augmented matrix can be row reduced to the given matrix. If requested also give the indicated solution. (a) 1 0 2 0 0 1 1 3 0 0 0 0 ± ± ± ± ± ± 1 - 2 0 (b) 1 - 1 2 0 3 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± 1 2 - 1
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Unformatted text preview: 3. (Problems 1.4.13 and 1.4.15 in text). Find all solutions of the given linear system, using the Gauss method with back-substitution. (a) 2 x-y = 8 6 x-5 y = 32 (b) y + z = 6 3 x-y + z =-7 x + y-3 z =-13 1 2 4. (Problem 1.4.25 in text). Determine whether the vector b = 3 5 3 is in the span of the vectors v 1 = 2 4 , v 2 = 1 4-2 , v 3 = -3-1 5...
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HW2 - 3. (Problems 1.4.13 and 1.4.15 in text). Find all...

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