2. Consider a linear system defined via AZ =7 where A is an m xn matrix, 7 is an n-column vector and is an m-column vector. Answer the following questions: (a) Assume that is not zero. For cach of the case: i. m > n, ii. m = n, iii. m

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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Pls solve part b
2. Consider a linear system defined via
AZ =
where A is an m xn matrix, 7 is an n-column vector and b is an m-column vector. Answer
the following questions:
(a) Assume that b is not zero. For cach of the case:
i. m > n,
ii. m = n,
iii. m <n,
indicate is it possible for the system to have
i. no solution,
ii. have a unique solution,
iii. have an infinite number of solutions.
(b) Repeate all of the above questions, for all of the above cases, but with = 0.
(c) Now consider the set of homogeous equations:
A7 =0
with matrix A given by
1
1
2
A = |2
1
3
- 3
3
- 5
Find all possible solutions for this system. Write them in terms of free parameters, if
necessary.
Transcribed Image Text:2. Consider a linear system defined via AZ = where A is an m xn matrix, 7 is an n-column vector and b is an m-column vector. Answer the following questions: (a) Assume that b is not zero. For cach of the case: i. m > n, ii. m = n, iii. m <n, indicate is it possible for the system to have i. no solution, ii. have a unique solution, iii. have an infinite number of solutions. (b) Repeate all of the above questions, for all of the above cases, but with = 0. (c) Now consider the set of homogeous equations: A7 =0 with matrix A given by 1 1 2 A = |2 1 3 - 3 3 - 5 Find all possible solutions for this system. Write them in terms of free parameters, if necessary.
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