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

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In summary: Q: In summary, the conversation discusses finding the inverse of a coefficient matrix, but the problem actually asks for the set of all triples that satisfy a given equation. The strategy is to solve a system of equations to find a particular solution.
  • #1
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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  • #2
Hi Shackleford! :smile:

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

[tex]T(a,b,c)=(1,11)[/tex]

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:

[tex]\left\{\begin{array}{c} a+b=1\\ 2a-c=11\\ \end{array}\right.[/tex]
 
  • #3
micromass said:
Hi Shackleford! :smile:

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

[tex]T(a,b,c)=(1,11)[/tex]

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:

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

Oh. Well, I quickly misread that problem. It's no problem now. I'll do it in the morning. Thanks!
 
  • #4
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.
 
  • #5
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.
 
  • #6
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
 

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

1. What is the purpose of determining T-inverse?

The purpose of determining T-inverse is to find the inverse of a matrix T. This is useful in solving systems of linear equations and performing other mathematical operations.

2. How is T-inverse calculated?

T-inverse is calculated by using the formula T-inverse = (1/det(T)) * adj(T), where det(T) is the determinant of matrix T and adj(T) is the adjugate of matrix T.

3. Can T-inverse be calculated for any matrix?

No, T-inverse can only be calculated for square matrices (nxn). In order for a matrix to have an inverse, it must have a non-zero determinant.

4. What is the significance of T-inverse?

The significance of T-inverse lies in its ability to solve systems of linear equations and perform other mathematical operations. It also allows for the transformation of coordinates and the simplification of complex calculations.

5. Are there any limitations to using T-inverse?

Yes, there are some limitations to using T-inverse. It can only be calculated for square matrices, and if the determinant of the matrix is zero, then the matrix does not have an inverse. Additionally, T-inverse may not always produce a unique solution to a system of equations.

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