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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 combination 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) 5. Do the vectors form a basis for R" ? If not a basis, can the vectors be used to find a basis for R"? If so, give an example of a basis. a. V = (1, 4, 5, 7, 9) V2 = (2,-1, 6, 8, 0) V3 = (6, 5, 8, 3, 2) V4=(-2,-3, 5, 8, 7) b. vị =(10, 5, 6)

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 combination 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) 5. Do the vectors form a basis for R" ? If not a basis, can the vectors be used to find a basis for R"? If so, give an example of a basis. a. V = (1, 4, 5, 7, 9) V2 = (2,-1, 6, 8, 0) V3 = (6, 5, 8, 3, 2) V4=(-2,-3, 5, 8, 7) b. vị =(10, 5, 6)

Advanced Engineering Mathematics
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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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) %3D 3. If possible, express t as a linear combination 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) 5. Do the vectors form a basis for R" ? If not a basis, can the vectors be used to find a basis for R"? If so, give an example of a basis. a. V = (1, 4, 5, 7, 9) V2 = (2,-1, 6, 8, 0) V3 = (6, 5, 8, 3, 2) V4=(-2,-3, 5, 8, 7) b. vị = (10, 5, 6) V2 = (1, 7, 4) V3 = (2, 2, 2) V4 = (9, 3, 6)
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) %3D 3. If possible, express t as a linear combination 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) 5. Do the vectors form a basis for R" ? If not a basis, can the vectors be used to find a basis for R"? If so, give an example of a basis. a. V = (1, 4, 5, 7, 9) V2 = (2,-1, 6, 8, 0) V3 = (6, 5, 8, 3, 2) V4=(-2,-3, 5, 8, 7) b. vị = (10, 5, 6) V2 = (1, 7, 4) V3 = (2, 2, 2) V4 = (9, 3, 6)
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