1 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 [00123 (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. iii) For the same A and B, find the special solutions to Ax=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= -1 3 5 -2 6 10 (b) B= |-1 -2 36 57
1 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 [00123 (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. iii) For the same A and B, find the special solutions to Ax=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= -1 3 5 -2 6 10 (b) B= |-1 -2 36 57
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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Reduce A and B to their triangular echelon forms U. Which variables are free?
[1 2 2 4 6]
2 3 69
0 1 2 3
2 4 2
(b) B = 0 4 4
088
(a) A = 1
0
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.
iii)
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.
(a) A=
-1 3 5
-2 6 10
(b) B=
|-1
-2
36
5
9].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7f238f8-1f46-4a1c-b609-d7342775b44d%2F644047e7-5550-4fbd-ab64-eddac7bf6a16%2Fomhl29o_processed.png&w=3840&q=75)
Transcribed Image Text:1
Reduce A and B to their triangular echelon forms U. Which variables are free?
[1 2 2 4 6]
2 3 69
0 1 2 3
2 4 2
(b) B = 0 4 4
088
(a) A = 1
0
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.
iii)
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.
(a) A=
-1 3 5
-2 6 10
(b) B=
|-1
-2
36
5
9].
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