(b) Consider a linear system Ax = b whose augmented matrix (A b) is a 6 xn matrix of rank k. where the natural numbers n and k satisfy n> 2 and k > 2, Answer the following questions, carefully explaining each answer. ) If k 5 and the system Ax b is inconsistent, what are the possible values that n can take? (i) If A take? 4 and the system Ax- b is consistent, what are the possible values that n can (iii) If A= 3 and the system Ax bhas infinitely many solutions, what are the possible values that n can take?
(b) Consider a linear system Ax = b whose augmented matrix (A b) is a 6 xn matrix of rank k. where the natural numbers n and k satisfy n> 2 and k > 2, Answer the following questions, carefully explaining each answer. ) If k 5 and the system Ax b is inconsistent, what are the possible values that n can take? (i) If A take? 4 and the system Ax- b is consistent, what are the possible values that n can (iii) If A= 3 and the system Ax bhas infinitely many solutions, what are the possible values that n can take?
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CT: Test
Problem 14CT
Related questions
Question
First image is the question and second is information on the matrices.

Transcribed Image Text:Question 1
(a)
Consider the flat Il, C R described by the vector parametric equation
0000
where s,teR
and the flat II, cR whose Cartesian description is given by the equations
where a and 3 are real constants.

Transcribed Image Text:(iii) If 3 and the system Ax
(b)
Consider a linear system Ax = b whose augmented matrix (A b) is a 6 x n matrix of rank k
where the natural numbersn and k satisfy n> 2 and k > 2.
Answer the following questions, carefully explaining each answer.
() Ifk=5 and the system Ax bis inconsistent, what are the possible values that n can
take?
(1i) If 4 and the system Ax b is consistent, what are the possible values that n can
take?
infinitely many solutions, what are the possible values
that n can take?
(iv) If the system Ax bhas at least two distinct solutions, what are the possible values that
IL can take?
(v) If the system Ax b has a unique solution, what are the possible values that can take?
# 日
a.
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