(a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor- mations L₁ and L2, respectively. (b) Write down expressions similar to the above for L₁ 0 L₂ and L₁ + L2, i.e. L₁ ° L2 (()) =???, (L₁+ L₂) ((1)) =??? (c) Hence compute the matrix B associated to L₁ 0 L₂ and the matrix C associated to L₁+ L2. Apply matrix algebra to show that B = A₁ A2 and
(a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor- mations L₁ and L2, respectively. (b) Write down expressions similar to the above for L₁ 0 L₂ and L₁ + L2, i.e. L₁ ° L2 (()) =???, (L₁+ L₂) ((1)) =??? (c) Hence compute the matrix B associated to L₁ 0 L₂ and the matrix C associated to L₁+ L2. Apply matrix algebra to show that B = A₁ A2 and
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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Transcribed Image Text:Consider the linear maps L₁, L2 : R³ → R³ defined as
22
~ (()) - () -(0)) - ()
L₁
L2
((
x + 3y
(a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor-
mations L₁ and L2, respectively.
(b) Write down expressions similar to the above for L₁ 0 L2 and L₁ + L2, i.e.
·(())-
"
L₁0 L2
=???, (L₁ + L₂)
(Ⓒ))
=???
1
(c) Hence compute the matrix B associated to L₁ 0 L₂ and the matrix C
associated to L₁+ L2. Apply matrix algebra to show that B = A₁ A₂ and
C = A₁ + A₂.
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