5 Aaron and Maya want to write the vector u = -5 as a linear comb -19 -2 1 V1 -2 V2 = 1 and V3 = 2 -1 -5 In other words, they are trying to calculate real numbers A1, A2 and X3 sue u = Av1 + A2V2 + A3v3. -1 -2 1 In order to do so, they decide to use the matrix A = -2 1 -1 -5 > with (LinearAlgebra) : > A := << -1,-2,-1 > |< -2,1,0 > |<1,2,-5 >>: > ATA := Transpose (A) .A; 9. AT A :=
5 Aaron and Maya want to write the vector u = -5 as a linear comb -19 -2 1 V1 -2 V2 = 1 and V3 = 2 -1 -5 In other words, they are trying to calculate real numbers A1, A2 and X3 sue u = Av1 + A2V2 + A3v3. -1 -2 1 In order to do so, they decide to use the matrix A = -2 1 -1 -5 > with (LinearAlgebra) : > A := << -1,-2,-1 > |< -2,1,0 > |<1,2,-5 >>: > ATA := Transpose (A) .A; 9. AT A :=
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
part a please

Transcribed Image Text:Aaron and Maya want to write the vector u=
-5
as a linear combination of
-19
--) --) - -)
2
1
Vị =
V2 =
1
and V3 =
In other words, they are trying to calculate real numbers A1, A2 and X3 such that
u= A1v1+ A2V2 + Agv3.
-1
-2
1
In order to do so, they decide to use the matrix A =
-2
1
2
and then they enter the following into Maple:
1
-5
> with (LinearAlgebra):
> A := << -1,-2,-1> |< -2,1,0>|<1,2,-5 >>:
> ATA := Transpose (A) .A;
6 0
AT A :=
0 5
0 0 30

Transcribed Image Text:(a)
Explain in the essay box below how the Maple output can be used to show that {v1, v2, V3} is a set of orthogonal vectors. Do not show all calculations,
just explain the ideas.
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