Let A be a m x n matrix, such that Ax = 0 has parametric solutions of the form x(s, t, u) = sX1 +tx2 +u x3 , where {x1, X2, X3} are the basic solutions provided by the gaussian algorithm. Which of the following are true? Select one or more: O dim[im(A)] = O dim[null(A)] : n – 3 = n – 3 O rank A = 3 O Ax = b is consistent for every b in R". O rank A = n – 3
Let A be a m x n matrix, such that Ax = 0 has parametric solutions of the form x(s, t, u) = sX1 +tx2 +u x3 , where {x1, X2, X3} are the basic solutions provided by the gaussian algorithm. Which of the following are true? Select one or more: O dim[im(A)] = O dim[null(A)] : n – 3 = n – 3 O rank A = 3 O Ax = b is consistent for every b in R". O rank A = n – 3
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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![Let A be a m x n matrix, such that Ax = 0 has parametric solutions of the form
x(s, t, u) = sX1 +tx2 +u x3 ,
where {x1, X2, X3} are the basic solutions provided by the gaussian algorithm. Which of the following are true?
Select one or more:
O dim[im(A)] =
O dim[null(A)] :
n – 3
= n – 3
O rank A = 3
O Ax = b is consistent for every b in R".
O rank A = n – 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F493972d6-49d1-40f5-bf68-00e16bd44a08%2Fbad0583c-c83f-4ba3-9ae2-aea7ee3f13df%2Fn4nykih_processed.png&w=3840&q=75)
Transcribed Image Text:Let A be a m x n matrix, such that Ax = 0 has parametric solutions of the form
x(s, t, u) = sX1 +tx2 +u x3 ,
where {x1, X2, X3} are the basic solutions provided by the gaussian algorithm. Which of the following are true?
Select one or more:
O dim[im(A)] =
O dim[null(A)] :
n – 3
= n – 3
O rank A = 3
O Ax = b is consistent for every b in R".
O rank A = n – 3
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