Matrix Solution and variable multiplication

Ali Asadullah
Messages
99
Reaction score
0
Can we multiply a row with a variable and add it with another row while solving homogeneous system of equations as a matrix?
 
Physics news on Phys.org
It might help if you gave an example of what you want to do. But I'm pretty sure the answer is yes, if it will help you solve the system (for example if the matrix has variable entries).
 
What do you mean by "variable"? If you have a system of equations in x, y, z, ..., then the matrix you use to solve the system is the matrix of coefficients, all numbers. It would make no sense to multiply by x, y, z, ...- and it would not help you to reduce the matrix.

But if you have a system of equations in x, y, z, ... where the coefficients depend on one or more parameters, they, yes, you might well want to multiply by those parameters.
 

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 Vector subspace and basis vectors in the context of data science
Replies
6
Views
3K
I Cycles from patterns in a permutation matrix
Replies
3
Views
2K
I Index notation of vector rotation
Replies
7
Views
2K
I Is tensor product the same as dyadic product of two vectors?
Replies
4
Views
3K
MHB Solving Systems of Six Equations with Nine Variables
Replies
1
Views
1K
I Matrix diagonalization algorithm
Replies
5
Views
2K
I Row space, Column space, Null space & Left null space
Replies
8
Views
3K
B Is it invalid to redefine the sgn function in this way in a proof?
Replies
15
Views
4K
MHB Matrix solutions with variable coefficient
Replies
1
Views
1K
MHB Creating Linearly Dependent Square Matrix from Cam Mechanism Equation
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top