Given the matrices: i) ii) 01 1 0 2 2 3 A 3 ^-(29) 8 - (-) -- »-( ) 01 B 0 = (²₂) D = 1 5 0 1 4 3 Show that (AB)C = A(BC) Find D-¹

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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a) Given the matrices:
i)
ii)
^= ( ²₂ )
A
1
01
0
B = 0 -1
- (₁ -²₁ ) C = (²) D = ( ²₁ ²)
3
Show that (AB)C: = A(BC)
Find D-¹
Transcribed Image Text:a) Given the matrices: i) ii) ^= ( ²₂ ) A 1 01 0 B = 0 -1 - (₁ -²₁ ) C = (²) D = ( ²₁ ²) 3 Show that (AB)C: = A(BC) Find D-¹
b) The forces acting on a link of an automated equipment in equilibrium are show
36 N
F₁
The equations for finding forces F₁ and F2 are given by:
i)
ii)
F₁+F₂ = 36
4F₁-5F₂ = 0
Write the equation in matrix form, AX=B.
F2
Find the values of F₁ and F2 using the relationship: X=A¹¹B.
Transcribed Image Text:b) The forces acting on a link of an automated equipment in equilibrium are show 36 N F₁ The equations for finding forces F₁ and F2 are given by: i) ii) F₁+F₂ = 36 4F₁-5F₂ = 0 Write the equation in matrix form, AX=B. F2 Find the values of F₁ and F2 using the relationship: X=A¹¹B.
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