An n x n matrix with two identical rows has infinitely many solutions

  • Thread starter Jamin2112
  • Start date
  • Tags
    Matrix
In summary, The problem is to prove the thread title using row reduction without using any information about rank, nullity, etc. The attempt at a solution involves subtracting identical rows and resulting in one of the rows being zero, leading to infinitely many solutions for the equation Ax = 0 where A is an n x n matrix. This means there are n-1 equations and n variables, resulting in an infinite number of solutions.
  • #1
Jamin2112
986
12

Homework Statement



Prove the thread title.

Homework Equations



Without using anything about rank, nullity, etc., --- just row reduction

The Attempt at a Solution



Can't figure this out. It's actually a friend one of my buddies is doing for his class. PLEASE ANSWER IN LESS THAN 2 HOURS! IT'S URGENT!
 
Physics news on Phys.org
  • #2
Well what will it mean if you subtract identical row 1 from the other identical row?
 
  • #3
rock.freak667 said:
Well what will it mean if you subtract identical row 1 from the other identical row?

One of the rows will now be zero
 
  • #4
infinitely many solutions to what?
 
  • #5
lanedance said:
infinitely many solutions to what?

Ax = 0 where A is an n x n matrix
 
  • #6
OK, so one of the rows is now zero, meaning the only information it gives us is 0=0. How many equations do you now have, and in how many variables?
 
  • #7
n - 1 equations and n variables ... meaning an infinite number of solutions.
 

FAQ: An n x n matrix with two identical rows has infinitely many solutions

What is an n x n matrix?

An n x n matrix is a rectangular array of numbers or variables arranged in rows and columns. The size of the matrix is determined by the number of rows (n) and the number of columns (n).

What does it mean for two rows to be identical in a matrix?

Two rows in a matrix are considered identical if they have the exact same entries in the same order. This means that the values in each position of the row are equal.

How can a matrix have infinitely many solutions?

A matrix with two identical rows has infinitely many solutions because there are multiple ways to express the same set of solutions. This is due to the fact that the two identical rows provide redundant information, allowing for different values in the remaining rows to still result in the same final solution.

Can a matrix with two identical rows have a unique solution?

No, a matrix with two identical rows cannot have a unique solution. This is because the two identical rows provide redundant information, resulting in an infinite number of solutions.

How can I determine the number of solutions for a matrix with two identical rows?

The number of solutions for a matrix with two identical rows can be determined by looking at the number of independent rows in the matrix. If there are two or more independent rows, there will be infinitely many solutions. If there is only one independent row, there will be a unique solution.

Similar threads

Back
Top