18. Consider the matrices 2 1 27 Xx₁ A = 2 2 -2 and X = X₂ 3 1 1 X3 a. Show that the equation Ax = x can be rewritten as (AI)x= 0 and use this result to solve Ax = x for x. b. Solve Ax = 4x. W
18. Consider the matrices 2 1 27 Xx₁ A = 2 2 -2 and X = X₂ 3 1 1 X3 a. Show that the equation Ax = x can be rewritten as (AI)x= 0 and use this result to solve Ax = x for x. b. Solve Ax = 4x. W
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
F1.6 Question 18 please write on paper
![4x₁
5x₂ + 8x3 = b₂
- 3x₁ + 3x₂-3x3 = b3
-4x₁ + 5x₂ + 2x3 = b₂
-4x₁ + 7x₂ + 4x3 = b3
-2x₁ + x₂ + 5x3 +
-3x₁ + 2x₂ + 2x3
X₂ + 3x3 + 2x₁ = b₁
x₁ = b₂
X₁ = b₂
4x₁3x₂ + x3 + 3x₁ = b₁
18. Consider the matrices
2
1
2
A = 2
2 -2 and
X = X₂
3
1
1
a. Show that the equation Ax = x can be rewritten as
(AI)x= 0 and use this result to solve Ax = x for x.
b. Solve Ax = 4x.
In Exercises 19-20, solve the matrix equation for X.
1
-1 1
2
-1
5
7 8
19. 2
3
0 X =
4
0
-3
0
1
0
2 -1]
3
5
-7
2
1
-2
11
[4 3
2
20.
0 -1 -1 X
6
7 8 9
1
1 -4
1
3 7 9]
Working with Proofs
21. Let Ax = 0 be a homogeneous system of n linear equations in
n unknowns that has only the trivial solution. Prove that if k
is any positive integer, then the system Akx = 0 also has only
the trivial solution.
22 Let Axr- 01
homogeneous system of n linear equations
17. X₁
-
W
T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccdd90b5-cd41-4340-8a36-15b102c9ba73%2Febea2747-400f-419e-98c7-51bf12afad7d%2Fj9t2q6n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4x₁
5x₂ + 8x3 = b₂
- 3x₁ + 3x₂-3x3 = b3
-4x₁ + 5x₂ + 2x3 = b₂
-4x₁ + 7x₂ + 4x3 = b3
-2x₁ + x₂ + 5x3 +
-3x₁ + 2x₂ + 2x3
X₂ + 3x3 + 2x₁ = b₁
x₁ = b₂
X₁ = b₂
4x₁3x₂ + x3 + 3x₁ = b₁
18. Consider the matrices
2
1
2
A = 2
2 -2 and
X = X₂
3
1
1
a. Show that the equation Ax = x can be rewritten as
(AI)x= 0 and use this result to solve Ax = x for x.
b. Solve Ax = 4x.
In Exercises 19-20, solve the matrix equation for X.
1
-1 1
2
-1
5
7 8
19. 2
3
0 X =
4
0
-3
0
1
0
2 -1]
3
5
-7
2
1
-2
11
[4 3
2
20.
0 -1 -1 X
6
7 8 9
1
1 -4
1
3 7 9]
Working with Proofs
21. Let Ax = 0 be a homogeneous system of n linear equations in
n unknowns that has only the trivial solution. Prove that if k
is any positive integer, then the system Akx = 0 also has only
the trivial solution.
22 Let Axr- 01
homogeneous system of n linear equations
17. X₁
-
W
T
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