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1. Explain why the following form linearly dependent sets of vec- tors. (Solve this problem by inspection.) (a) u = (-1, 2, 4) and uz = (5, – 10, -20) in R %3D 6. (b) u, = (3,-1), u2 = (4, 5), u3 = (-4, 7) in R² %3D %3D (c) P, = 3-2x + x² and p, = 6 – 4x + 2x² in P2 -3 4 3 (d) A = 2 in M22 and B = -2

1. Explain why the following form linearly dependent sets of vec- tors. (Solve this problem by inspection.) (a) u = (-1, 2, 4) and uz = (5, – 10, -20) in R %3D 6. (b) u, = (3,-1), u2 = (4, 5), u3 = (-4, 7) in R² %3D %3D (c) P, = 3-2x + x² and p, = 6 – 4x + 2x² in P2 -3 4 3 (d) A = 2 in M22 and B = -2

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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Can you please help me with these three questions (1,2,3) please? It's about Linear Independence.

Explain why the following form linearly dependent sets of vec- 米1 tors. (Solve this problem by inspection.) (a) u = (-1, 2, 4) and u2 = (5, -10, -20) in R %3D %3D (b) u, = (3,-1), u2 = (4, 5), u3 = (-4, 7) in R? %3D %3D %3D (c) P, = 3-2x+x² and p, = 6 – 4x + 2x² in P2 3 4 3 - (d) A = and B = -2 in M22 2 0
Transcribed Image Text:Explain why the following form linearly dependent sets of vec- 米1 tors. (Solve this problem by inspection.) (a) u = (-1, 2, 4) and u2 = (5, -10, -20) in R %3D %3D (b) u, = (3,-1), u2 = (4, 5), u3 = (-4, 7) in R? %3D %3D %3D (c) P, = 3-2x+x² and p, = 6 – 4x + 2x² in P2 3 4 3 - (d) A = and B = -2 in M22 2 0
2. In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in R. (a) (-3, 0, 4), (5, –1, 2), (1, 1, 3) (b) (-2, 0, 1), (3, 2, 5), (6, –1, 1), (7,0, –2) 3. In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in R4. (a) (3, 8, 7, –3), (1, 5, 3, –1), (2, -1, 2, 6), (4, 2, 6, 4) (b) (3, 0, –3, 6), (0, 2, 3, 1), (0, -2, -2, 0), (-2, 1, 2, 1)
Transcribed Image Text:2. In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in R. (a) (-3, 0, 4), (5, –1, 2), (1, 1, 3) (b) (-2, 0, 1), (3, 2, 5), (6, –1, 1), (7,0, –2) 3. In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in R4. (a) (3, 8, 7, –3), (1, 5, 3, –1), (2, -1, 2, 6), (4, 2, 6, 4) (b) (3, 0, –3, 6), (0, 2, 3, 1), (0, -2, -2, 0), (-2, 1, 2, 1)
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