Reduce A and B to their triangular echelon forms U. Which variables are free? [242] [1 2 2 4 6 (a) A = 1 2 3 69 0 0 1 2 3 (b) B= 0 4 4. 088 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 Requals 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.
Reduce A and B to their triangular echelon forms U. Which variables are free? [242] [1 2 2 4 6 (a) A = 1 2 3 69 0 0 1 2 3 (b) B= 0 4 4. 088 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 Requals 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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 21EQ: Students frequently perform the following type of calculation to introduce a zero into a matrix:...
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I need help with the following please parts i to iv
![Reduce A and B to their triangular echelon forms U. Which variables are free?
[2 4 2
[1 2 2 4 6
(a) A = 1 2 3 69
0 0 1 2 3
(b) B= 0 44
088
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.
(a) A =
5]
-1
3
-2 6 10
(b) B =
-1
-2
36
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7f238f8-1f46-4a1c-b609-d7342775b44d%2Fc3107682-3ac6-4913-873b-f8efb12c8692%2Feecvryw_processed.png&w=3840&q=75)
Transcribed Image Text:Reduce A and B to their triangular echelon forms U. Which variables are free?
[2 4 2
[1 2 2 4 6
(a) A = 1 2 3 69
0 0 1 2 3
(b) B= 0 44
088
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.
(a) A =
5]
-1
3
-2 6 10
(b) B =
-1
-2
36
5
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