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Orthogonal Matrix Multiplication Problem 18: Given an orthogonal matrix A, compute AT A, where AT is the transpose of A. Verify that the result is the identity matrix. [0.5 -0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 0.5 0.5 Problem 19: Now compute A. AT, and confirm that this result is also the same as the previous problem. Dot Product Problem 20: Consider two 7× 1 matrices, u and v. First, compute u. v. Next, compute uv. Show that the results of these two computations are the same. U = -3 8 12 -13 7 9 4 V= 7 14

Orthogonal Matrix Multiplication Problem 18: Given an orthogonal matrix A, compute AT A, where AT is the transpose of A. Verify that the result is the identity matrix. [0.5 -0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 0.5 0.5 Problem 19: Now compute A. AT, and confirm that this result is also the same as the previous problem. Dot Product Problem 20: Consider two 7× 1 matrices, u and v. First, compute u. v. Next, compute uv. Show that the results of these two computations are the same. U = -3 8 12 -13 7 9 4 V= 7 14

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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Orthogonal Matrix Multiplication Problem 18: Given an orthogonal matrix A, compute AT A, where AT is the transpose of A. Verify that the result is the identity matrix. 0.5 -0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 0.5 0.5 Problem 19: Now compute A AT, and confirm that this result is also the same as the previous problem. Dot Product Problem 20: Consider two 7x1 matrices, u and v. First, compute u.v. Next, compute uvT. Show that the results of these two computations are the same. U= -3 8 12 -13 9 4 V= 7 14 5
Transcribed Image Text:Orthogonal Matrix Multiplication Problem 18: Given an orthogonal matrix A, compute AT A, where AT is the transpose of A. Verify that the result is the identity matrix. 0.5 -0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 0.5 0.5 Problem 19: Now compute A AT, and confirm that this result is also the same as the previous problem. Dot Product Problem 20: Consider two 7x1 matrices, u and v. First, compute u.v. Next, compute uvT. Show that the results of these two computations are the same. U= -3 8 12 -13 9 4 V= 7 14 5
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