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A7 = %3D where A is an m × n 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 each of the case: i. т> п, i. m 3D п, iii. т <п, indicate is it possible for the system to have i. no solution, ii. have a unique solution, iii. have an infinite number of solutions.

A7 = %3D where A is an m × n 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 each of the case: i. т> п, i. m 3D п, iii. т <п, indicate is it possible for the system to have i. no solution, ii. have a unique solution, iii. have an infinite number of solutions.

Advanced Engineering Mathematics
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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pls solve the question in the image below

2. Consider a linear system defined via AT = 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 each of the case: i. т > п, ii. m = n, ii. m < п, 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 6 = 0. (c) Now consider the set of homogeous equations: Aहे = 0 with matrix A given by 1 1 2 - 2 A = 1 3 - 3 3 2 - 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 AT = 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 each of the case: i. т > п, ii. m = n, ii. m < п, 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 6 = 0. (c) Now consider the set of homogeous equations: Aहे = 0 with matrix A given by 1 1 2 - 2 A = 1 3 - 3 3 2 - 5 Find all possible solutions for this system. Write them in terms of free parameters, if necessary.
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