Please use Mathematica to solve the problems below. 1. Given vectors u = (1,5) and v = (- 3,7), answer the following. a) Are vectors u and v linearly independent or linearly dependent? Support your answer. b) If possible, express w = (2, 10) as a linear combination of u and v 2. Determine if the following vectors are linearly independent or dependent. If linearly dependent, find scalars a, b, and c such that au+bv+cw=0. u = (1, 1,0, 4, 5), v = (5,1,3,–2, 1), and w = (0, 1,2, 3, 6) 3. If possible, express t as a linear combínation of u, v, and w. t = (3, 1, 5), u= (1,5, 8), v = (5, 2, 17), and w = (6,– 10, 8) 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), u = (1,2, 1), v = (- 2,– 1,– 1), and w = (1,-4,– 1)
Please use Mathematica to solve the problems below. 1. Given vectors u = (1,5) and v = (- 3,7), answer the following. a) Are vectors u and v linearly independent or linearly dependent? Support your answer. b) If possible, express w = (2, 10) as a linear combination of u and v 2. Determine if the following vectors are linearly independent or dependent. If linearly dependent, find scalars a, b, and c such that au+bv+cw=0. u = (1, 1,0, 4, 5), v = (5,1,3,–2, 1), and w = (0, 1,2, 3, 6) 3. If possible, express t as a linear combínation of u, v, and w. t = (3, 1, 5), u= (1,5, 8), v = (5, 2, 17), and w = (6,– 10, 8) 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), u = (1,2, 1), v = (- 2,– 1,– 1), and w = (1,-4,– 1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Please use Mathematica to solve the problems below.
1. Given vectors u= (1,5) and v = (- 3,7), answer the following.
a) Are vectors u and v linearly independent or linearly dependent? Support your answer.
b) If possible, express w = (2, 10) as a linear combination of u and v
2. Determine if the following vectors are linearly independent or dependent. If linearly
dependent, find scalars a, b, and c such that au+bv+cw=0.
u = (1, 1,0, 4, 5), v = (5,1,3,–2, 1), and w = (0, 1,2, 3, 6)
3. If possible, express t as a linear combínation of u, v, and w.
t = (3, 1, 5), u= (1,5, 8), v = (5, 2, 17), and w = (6,– 10, 8)
4. If possible, express t as a linear combination of u, v, and w.
t = (2, 13, 5), u = (1,2, 1), v = (- 2,– 1,– 1), and w = (1,-4,– 1)
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