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´0 -1) A= |0 1 . 1 2 3 4 1 1 -2 1 and B= 1

´0 -1) A= |0 1 . 1 2 3 4 1 1 -2 1 and B= 1

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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Consider the matrices 0 -1 (G 1 2 3 1 1 4 A = 1 and B= -2 0 1 1 a) Compute AB. b) Partition A into rows and B into columns as aj and B= ( b, |b | ba | b) ( bị |b2 | b3 | b4 ) A = a2 az Verify directly that i) AB = ( Abı Ab2 Ab3 Ab4) ii) aB a, B AB = azB c) Partition AT into columns: AT = ( u | u2 | us ) and let C = ( (u{B)" | (u}B)" | (u{ B)" ) How many rows and columns does C have? d) Express C in terms of A and B. e) Write out the column--row expansion of C.
Transcribed Image Text:Consider the matrices 0 -1 (G 1 2 3 1 1 4 A = 1 and B= -2 0 1 1 a) Compute AB. b) Partition A into rows and B into columns as aj and B= ( b, |b | ba | b) ( bị |b2 | b3 | b4 ) A = a2 az Verify directly that i) AB = ( Abı Ab2 Ab3 Ab4) ii) aB a, B AB = azB c) Partition AT into columns: AT = ( u | u2 | us ) and let C = ( (u{B)" | (u}B)" | (u{ B)" ) How many rows and columns does C have? d) Express C in terms of A and B. e) Write out the column--row expansion of C.
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