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

[Shackleford]

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

 

[micromass]

Hi Shackleford!

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.

 

[Shackleford]

Hi Shackleford!

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!

 

[Shackleford]

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.

K_H = 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.

 

[acsman123]

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.

 

[Ray Vickson]

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