Problem 5 Consider A = (1) Compute T^([])? = -17 TA ? Let us denote ])? Is there any relation between T^([]) and [1]? (2) Compute TA([3] ])? Is there any relation between TA([]) and []? Let us denote √₂ = (3) Compute TA([])? Is there any relation between TA([]) and | [}]? ? Let us denote √3 = (4) Show that R3 = Span(1, 2, 3). (5) Decompose ₁ = [] in terms of 1, 2, 3. (6) Give an expression of TAK (1) in terms of k, 1, 2, 3 (and some scalars). hint: one can use Problem 4 (3) and (4) of Homework 5. (7) Define P= -I 0 (8) Let D= 0-10 . Compute P-1 Check that AP.D. P-1. (9) Give the general form of DD.D....D for n ≥ 1. In times (10) Show that for any n≥ 1, A" P.D" P-1. hint: try to compute A2, which is just (P. D. P-1) (P. D. P-1) (11) Write down the general form of A" for n ≥ 1.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Linear algebra: please solve at least first 5 parts correctly and handwritten also write problem Number before starting the question 

Problem 5 Consider A =
(1) Compute T^([])?
=
-17
TA
? Let us denote
])? Is there any relation between T^([]) and [1]?
(2) Compute TA([3] ])? Is there any relation between TA([]) and []? Let us denote
√₂ =
(3) Compute TA([])? Is there any relation between TA([]) and | [}]? ? Let us denote
√3 =
(4) Show that R3 = Span(1, 2, 3).
(5) Decompose ₁ =
[]
in terms of 1, 2, 3.
(6) Give an expression of TAK (1) in terms of k, 1, 2, 3 (and some scalars).
hint: one can use Problem 4 (3) and (4) of Homework 5.
(7) Define P=
-I 0
(8) Let D=
0-10
. Compute P-1
Check that AP.D. P-1.
(9) Give the general form of DD.D....D for n ≥ 1.
In times
(10) Show that for any n≥ 1, A" P.D" P-1.
hint: try to compute A2, which is just (P. D. P-1) (P. D. P-1)
(11) Write down the general form of A" for n ≥ 1.
Transcribed Image Text:Problem 5 Consider A = (1) Compute T^([])? = -17 TA ? Let us denote ])? Is there any relation between T^([]) and [1]? (2) Compute TA([3] ])? Is there any relation between TA([]) and []? Let us denote √₂ = (3) Compute TA([])? Is there any relation between TA([]) and | [}]? ? Let us denote √3 = (4) Show that R3 = Span(1, 2, 3). (5) Decompose ₁ = [] in terms of 1, 2, 3. (6) Give an expression of TAK (1) in terms of k, 1, 2, 3 (and some scalars). hint: one can use Problem 4 (3) and (4) of Homework 5. (7) Define P= -I 0 (8) Let D= 0-10 . Compute P-1 Check that AP.D. P-1. (9) Give the general form of DD.D....D for n ≥ 1. In times (10) Show that for any n≥ 1, A" P.D" P-1. hint: try to compute A2, which is just (P. D. P-1) (P. D. P-1) (11) Write down the general form of A" for n ≥ 1.
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