xample: Solving Axb, Ux = c, and Rx = d 1x1 + 2x2 + 3x3 + 5x4 Ax=b is 2x₁ + 4x2 + 8x3 + 12x4 = 3x₁ + 6x2 + 7x3 + 13x4 = 4- bi b2 b3 1. Reduce [A b] to [U c], to reach a triangular system Ux = c. 2. Find the condition on b₁, b₂, b3 to have a solution. 3. Describe the column space of 4: Which plane in R³? 4. Describe the nullspace of A: Which special solutions in R4? 5. Find a particular solution to Ax=(0;6;-6) and the complete x+x. 6. Reduce [Uc] to [R d]: Special solutions from R and. Xp from d.
xample: Solving Axb, Ux = c, and Rx = d 1x1 + 2x2 + 3x3 + 5x4 Ax=b is 2x₁ + 4x2 + 8x3 + 12x4 = 3x₁ + 6x2 + 7x3 + 13x4 = 4- bi b2 b3 1. Reduce [A b] to [U c], to reach a triangular system Ux = c. 2. Find the condition on b₁, b₂, b3 to have a solution. 3. Describe the column space of 4: Which plane in R³? 4. Describe the nullspace of A: Which special solutions in R4? 5. Find a particular solution to Ax=(0;6;-6) and the complete x+x. 6. Reduce [Uc] to [R d]: Special solutions from R and. Xp from d.
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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![Solving Ax = b, Ux = c, and Rx = d
Example:
1x + 2x2 + 3x3 +
5x4
Ax =b is
2.x1 + 4x2 + 8x3 + 12x4
b2
%3D
3x1 + 6x2 + 7x3 + 13x4
b3
1. Reduce [A b] to [U c], to reach a triangular system Ux c.
2. Find the condition on b,, b,, b, to have a solution.
3. Describe the column space of A: Which plane in R3?
4. Describe the nullspace of A: Which special solutions in R'4?
5. Find a particular solution to Ax = (0;6;-6) and the complete x, tx,.
6. Reduce [U c] to [R d]: Special solutions from R and x, from d.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5b67683-7b22-45f4-8ede-58ec3c63e68d%2F6db9ce67-405e-4346-b03f-541d71db4967%2F32pldur_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solving Ax = b, Ux = c, and Rx = d
Example:
1x + 2x2 + 3x3 +
5x4
Ax =b is
2.x1 + 4x2 + 8x3 + 12x4
b2
%3D
3x1 + 6x2 + 7x3 + 13x4
b3
1. Reduce [A b] to [U c], to reach a triangular system Ux c.
2. Find the condition on b,, b,, b, to have a solution.
3. Describe the column space of A: Which plane in R3?
4. Describe the nullspace of A: Which special solutions in R'4?
5. Find a particular solution to Ax = (0;6;-6) and the complete x, tx,.
6. Reduce [U c] to [R d]: Special solutions from R and x, from d.
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