2. Use matrix multiplication to find the orthogonal projection of(1, 2, - 3) onto theа. ху-plane.b. xz-plane.O Type here to search55°F Sun國Gp

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Answered: 2. Use matrix multiplication to find…

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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Describe the solutions of x1 + 2x2 – 3x3 = 5, 2x1 + x2 – 3x3 = 13, and -x1 + x2 = -8 in parametric vector form, and provide a geometric comparison with the solution set in x1 + 2x2 — Зx3 — 0, 2х1 + х2 — Зхз — 0, and — х1 + X2 — 0. |
Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is translation by (1, 4, 3). To blow up the picture around the center point (1, 4, 3), would you use vST or vT S?
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2. In a dance performance, four dancers form a diamond with vertices A(2, 0), B(0, 2), C(-2, 0), and D(0, – 2). Then, they move along the dance floor following the translation vector, (0, 4). There they pause, and then move again along the same vector. What are their coordinates after six such translations? а. 4(26, 24), В'(24, 6), С'(22, 24), аnd D'(24, 22) b. А(2, 10), B' (0, 12), С'(-2, 10), and D' (0, 8) c. A'(2, 24), B' (0, 26), C'(-2, 24), and D'(0, 22) d. A'(26, 0), B'(24, 2), C'(22, 0), and D'(24, --2)

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2. Use matrix multiplication to find the orthogonal projection of (1, 2, - 3) onto the a. ху-plane. b. xz-plane.