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Problem No.1 Let A=1 -2 3 and B= 1 Find AB and BA -4 2 5 -1 4

Problem No.1 Let A=1 -2 3 and B= 1 Find AB and BA -4 2 5 -1 4

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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Problem No.1 Let A= 1 -2 3 and B= 1 3 Find AB and BA -4 2 5 -1 4 Problem No.2 Let A= 1 -1 and a) Find the product AB b) Show that A³ = 4A B= 1 3 5 -1 1 3 1 Problem No.3 Let 2 -3 -5 -1 3 5 2 -2 -4 A= -1 1 -3 -5 C= -1 1 -3 4 5 B= 3 4 1 -3 -4 -1 3 5 -4 Find: а) АВ b) ВА с) ВС d) СВ e) САВ f) СТ АВ g) (AB)™C h) СТС i) ЗА + 4B 50 j) C² – B? + A? – 3 I -
Transcribed Image Text:Problem No.1 Let A= 1 -2 3 and B= 1 3 Find AB and BA -4 2 5 -1 4 Problem No.2 Let A= 1 -1 and a) Find the product AB b) Show that A³ = 4A B= 1 3 5 -1 1 3 1 Problem No.3 Let 2 -3 -5 -1 3 5 2 -2 -4 A= -1 1 -3 -5 C= -1 1 -3 4 5 B= 3 4 1 -3 -4 -1 3 5 -4 Find: а) АВ b) ВА с) ВС d) СВ e) САВ f) СТ АВ g) (AB)™C h) СТС i) ЗА + 4B 50 j) C² – B? + A? – 3 I -
Problem No.4 If 2 1 3 show that A3 - 2A? - 9A = 0 but A? - 2A - 9 I# 0 A= 1 -1 2 1 2 1 Problem No.5 0 0 0 1 0 0 0 1 0 If 1 A= 0 0 1 0 0 0 and Calculate the products AB and BA and show that A? B + B? A = A B=
Transcribed Image Text:Problem No.4 If 2 1 3 show that A3 - 2A? - 9A = 0 but A? - 2A - 9 I# 0 A= 1 -1 2 1 2 1 Problem No.5 0 0 0 1 0 0 0 1 0 If 1 A= 0 0 1 0 0 0 and Calculate the products AB and BA and show that A? B + B? A = A B=
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