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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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1. Consider the two linear functions h: R3 → P2 and g: P2 → M22 given as here. рр-2g 9. H (a + b)x² + (2a + 26)x + c px + qx + rH с Use these bases for the spaces. (o 2 B = (| 1 ) C = (1+x,1– x, x²) D= 3 (a) Give the formula composition map go h: R³ → M22 directly from the above definition. Following the definitions gives this. a H (a + b)x² + (2a + 26)x + c a + b 2а + 26 (a + b) – 2(2a + 26) \ a +b 2а + 2b — За — 3b (b) Represent h and g with respect to the appropriate bases. Весause 0, 0, H 2x2 + 4x+1 1 H x2 + 2x +1 H Ox2 + 0x +1 (1) 1 we get this representation for h. 3/2 1/2) 5/2 -3/2 -1/2 1/2 RepB,c(h) = 2 1 Similarly, because (4 ) *- (C ) -2 1+ xH 1- xH 1 this is the representation of g. 1 -1 Repc,D(9) = 1/2 1/3 -1/3 1
Transcribed Image Text:1. Consider the two linear functions h: R3 → P2 and g: P2 → M22 given as here. рр-2g 9. H (a + b)x² + (2a + 26)x + c px + qx + rH с Use these bases for the spaces. (o 2 B = (| 1 ) C = (1+x,1– x, x²) D= 3 (a) Give the formula composition map go h: R³ → M22 directly from the above definition. Following the definitions gives this. a H (a + b)x² + (2a + 26)x + c a + b 2а + 26 (a + b) – 2(2a + 26) \ a +b 2а + 2b — За — 3b (b) Represent h and g with respect to the appropriate bases. Весause 0, 0, H 2x2 + 4x+1 1 H x2 + 2x +1 H Ox2 + 0x +1 (1) 1 we get this representation for h. 3/2 1/2) 5/2 -3/2 -1/2 1/2 RepB,c(h) = 2 1 Similarly, because (4 ) *- (C ) -2 1+ xH 1- xH 1 this is the representation of g. 1 -1 Repc,D(9) = 1/2 1/3 -1/3 1
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