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relative to the coordinate axes is clockwise through an angle of "/3. 5. In R³ let A = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and let A' = {(0, 1, 1), (1, 0, 1), (1, 1, 0)}. Find the matrix of transition P from A to A' and the matrix of transition P-¹ from A' to A.

relative to the coordinate axes is clockwise through an angle of "/3. 5. In R³ let A = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and let A' = {(0, 1, 1), (1, 0, 1), (1, 1, 0)}. Find the matrix of transition P from A to A' and the matrix of transition P-¹ from A' to A.

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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relative to the coordinate axes is clockwise through an angle of "/3. 5. In R³ let A = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and let A' = {(0, 1, 1), (1, 0, 1), (1, 1, 0)}. Find the matrix of transition P from A to A' and the matrix of transition P-1 from A' to A. 6. Let A, B, and C be three bases of V. Let P be the matrix of transition from A to B and let Q be the matrix of transition from B to C. Is PQ or QP the matrix of transition from A to C? Compare the order of multiplication of matrices of transi- tion and matrices representing linear transformation. 7. Use the results of Exercise 6 to resolve the question raised in the parenthetical remark of Exercise 3, and implicitly assumed in Exercise 5. If P is the matrix of transition from A to A' and Q is the matrix of transition from A' to A, show that PQ = I.
Transcribed Image Text:relative to the coordinate axes is clockwise through an angle of "/3. 5. In R³ let A = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and let A' = {(0, 1, 1), (1, 0, 1), (1, 1, 0)}. Find the matrix of transition P from A to A' and the matrix of transition P-1 from A' to A. 6. Let A, B, and C be three bases of V. Let P be the matrix of transition from A to B and let Q be the matrix of transition from B to C. Is PQ or QP the matrix of transition from A to C? Compare the order of multiplication of matrices of transi- tion and matrices representing linear transformation. 7. Use the results of Exercise 6 to resolve the question raised in the parenthetical remark of Exercise 3, and implicitly assumed in Exercise 5. If P is the matrix of transition from A to A' and Q is the matrix of transition from A' to A, show that PQ = I.
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