Reduce A and B to their triangular echelon forms U. Which variables are free? [1 2 2 4 6] 2 3 69 [00123] [242] (b) B= 0 4 4 08 (a) A 1 For the matrices in Problem 1, find a special solution for each free variable. (Set the free variable to 1. Set the other free variables to zero.) By further row operations on each U in Problem 1, find the reduced echelon form R. True or false with a reason: The nullspace of R equals the nullspace of U. For the same A and B, find the special solutions to Ax=0 and Ba=0. For an m by n matrix, the number of pivot variables plus the number of free variables is This is the Counting Theorem:r + (n -r) = n.
Reduce A and B to their triangular echelon forms U. Which variables are free? [1 2 2 4 6] 2 3 69 [00123] [242] (b) B= 0 4 4 08 (a) A 1 For the matrices in Problem 1, find a special solution for each free variable. (Set the free variable to 1. Set the other free variables to zero.) By further row operations on each U in Problem 1, find the reduced echelon form R. True or false with a reason: The nullspace of R equals the nullspace of U. For the same A and B, find the special solutions to Ax=0 and Ba=0. For an m by n matrix, the number of pivot variables plus the number of free variables is This is the Counting Theorem:r + (n -r) = n.
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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I need help with this parts a to d please
![Reduce A and B to their triangular echelon forms U. Which variables are free?
[242]
[1 2 2 4 67
(a) A = 1 2 3 69
(b) B= 0 44
088
0 0 1 2 3
For the matrices in Problem 1, find a special solution for each free variable. (Set the
free variable to 1. Set the other free variables to zero.)
By further row operations on each U in Problem 1, find the reduced echelon form R.
True or false with a reason: The nullspace of R equals the nullspace of U.
For the same A and B, find the special solutions to Ar=0 and Br=0. For an m by
n matrix, the number of pivot variables plus the number of free variables is
This is the Counting Theorem:r + (n -r) = n.
(b) B=
(a) A =
-1 3 5
-2
6 10
.
36
-1
-2
3 5
6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F804b524f-1358-4abb-a7b5-3c68d6fe70c2%2F217d8005-c288-4dc9-8d3b-f924702dec4f%2Fglcg6r_processed.png&w=3840&q=75)
Transcribed Image Text:Reduce A and B to their triangular echelon forms U. Which variables are free?
[242]
[1 2 2 4 67
(a) A = 1 2 3 69
(b) B= 0 44
088
0 0 1 2 3
For the matrices in Problem 1, find a special solution for each free variable. (Set the
free variable to 1. Set the other free variables to zero.)
By further row operations on each U in Problem 1, find the reduced echelon form R.
True or false with a reason: The nullspace of R equals the nullspace of U.
For the same A and B, find the special solutions to Ar=0 and Br=0. For an m by
n matrix, the number of pivot variables plus the number of free variables is
This is the Counting Theorem:r + (n -r) = n.
(b) B=
(a) A =
-1 3 5
-2
6 10
.
36
-1
-2
3 5
6
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