Finding Solutions for a Matrix with Variables: Row Reduction Required?

  • Thread starter Thread starter rhuelu
  • Start date Start date
  • Tags Tags
    Matrix Variables
rhuelu
Messages
17
Reaction score
0
here's a tough one...

find the values of x for which the matric has no, one, and inf many solutions

A= (1 -2 3 1; 2 x 6 6; -1 -3 x-3 0)
 
Physics news on Phys.org
What do all those mean to you? I.e. what properties does a matrix that has no solutions have? What about one solution? What about infinitely many? You can think of these geometrically, what does it mean (geometricall) to have no solutions? one? infinitely many?
 
What have you done? If you want, as your title implies the the "row reduced echelon form", then go ahead and do the row reduction! The fact that "x" is a variable only means you have to use a little algebra rather than just arithmetic. That probably will involve fractions that have some function of x as the denominator. Obviously, values of x that make the denominator 0 will give difficulties.

I do feel compelled to point out that a matrix doesn't have a "solution". If you are asking for which values of x does the matrix equation has one, no, or infinitely many solutions, you will have to have an equation!
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Row space, Column space, Null space & Left null space
Replies
8
Views
3K
MHB Matrix solutions with variable coefficient
Replies
1
Views
1K
MHB 307.1.1 Use row reduction on the appropriate augmented
Replies
5
Views
1K
MHB Could you prove that f(A)>=0 whenever A>0?
Replies
6
Views
1K
I Jacobi matrix diagonalization problems
Replies
5
Views
2K
I Want to understand how to express the derivative as a matrix
Replies
8
Views
2K
MHB Define matrix to get a row operation of type 1
Replies
2
Views
1K
A How to augment a machine learning matrix?
Replies
10
Views
2K
B Row reduction, Gaussian Elimination on augmented matrix
Replies
6
Views
2K
I Matrix diagonalization algorithm
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top