How Do You Find the Inverse of a Non-Square Matrix?

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Homework Help Overview

The discussion revolves around finding the inverse of a non-square matrix, specifically in the context of a transformation represented by a linear mapping. The original poster initially attempts to find the inverse of a 2x3 coefficient matrix and later addresses a related problem involving a system of equations.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the problem, clarifying that the task is to find a set of solutions rather than a unique inverse. There are attempts to solve a system of equations derived from the transformation, with some participants questioning the interpretation of the problem statement.

Discussion Status

The discussion is active, with participants providing insights and clarifications about the problem requirements. Some guidance has been offered regarding the nature of the solutions expected, and there is recognition of the need to solve a system of equations. Multiple interpretations of the problem are being explored.

Contextual Notes

There is mention of a misunderstanding regarding the problem's requirements, as well as the potential for multiple solutions to the equations presented. The context includes a focus on linear transformations and their properties.

Shackleford
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I thought that I could find the inverse of the coefficient matrix, but it's originally 2x3, so I redacted the linearly dependent row and found the 2x2 A inverse. I'm not sure what to do after that.

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110625_165538.jpg

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110625_170257.jpg
 
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Hi Shackleford! :smile:

The problem is not asking you to determine the inverse of T. The problem is asking you to calculate T^{-1}(1,11) which is the set of all triples (a,b,c) such that

T(a,b,c)=(1,11)

There will NOT be a unique (a,b,c) that satisfies this (in general). We will expect a set of triples as answer.

The equation brings us to a system of equations that you need to solve:

\left\{\begin{array}{c} a+b=1\\ 2a-c=11\\ \end{array}\right.
 
micromass said:
Hi Shackleford! :smile:

The problem is not asking you to determine the inverse of T. The problem is asking you to calculate T^{-1}(1,11) which is the set of all triples (a,b,c) such that

T(a,b,c)=(1,11)

There will NOT be a unique (a,b,c) that satisfies this (in general). We will expect a set of triples as answer.

The equation brings us to a system of equations that you need to solve:

\left\{\begin{array}{c} a+b=1\\ 2a-c=11\\ \end{array}\right.

Oh. Well, I quickly misread that problem. It's no problem now. I'll do it in the morning. Thanks!
 
The strategy is to find the set of solutions to the homogeneous equation and then find a particular solution.

a + b = 1
2a - c = 11

a + b = 0
2a - c = 0

Implies a = a, b = -a, c = 2a.

KH = a(1, -1, 2)

Solving the system yields

a -(1/2)c = 11/2
b -(1/2)c = -9/2

The book's answer sets c = 0 and gives the particular solution as (11/2, -9/2, 0). Not too difficult a problem. It's a good problem to test your fundamental understanding of the theory and technique.
 
my daughter is studying in Class XI in a AP board school with BiPC.She is struggling to find the value of Tan inverse 4. Pl help.
 
Do you mean arctan(4) or tan(1/4)? I can read your question either way. Also: what angular units are used (degrees? radians?).

RGV
 

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