- #1

MurdocJensen

- 47

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter MurdocJensen
- Start date

In summary, if you have a square, noninvertible matrix (like A in the example), then reducing the matrix will always yield at least one row of zeroes. If you have an augmented matrix where the last column is not 0, then there exist an infinite number of solutions.

- #1

MurdocJensen

- 47

- 0

Physics news on Phys.org

- #2

Mark44

Mentor

- 37,745

- 10,089

A

A

In both equations I'm assuming that A is a square, noninvertible matrix (i.e., |A| = 0).

Because |A| = 0, row reducing A will yield at least one row whose entries are all zero. This means that we have a system of equations with fewer equation than variables, meaning that at least one variable is free, so there are an infinite number of solutions for

If we represent the second matrix equation by an augmented matrix, row reducing A will still yield at least one row of zeroes on the left side of the augmented matrix. If the element of b that corresponds to that zero row is not zero, that row of the augmented matrix represents the equation

0x

- #3

HallsofIvy

Science Advisor

Homework Helper

- 42,988

- 975

- #4

MurdocJensen

- 47

- 0

quickreply: i want to post an example system. anyone know how to type and copy matrices?

- #5

blue_raver22

- 2,250

- 0

The fact that a matrix is singular, meaning it has no inverse, indicates that the system of equations it represents has either no solution or an infinite number of solutions. In order to determine which of these scenarios is the case, we can look at the reduced row echelon form (RREF) of the matrix.

If the RREF of the matrix has a row of all zeros, then the system has no solution. This is because in the RREF, this row represents an equation such as 0x + 0y + 0z = k, where k is a non-zero number. This is impossible to satisfy, as any value for x, y, or z will result in 0 on the left side of the equation, not k.

On the other hand, if the RREF of the matrix has no rows of all zeros, then the system has an infinite number of solutions. This is because in the RREF, each non-zero row represents an equation such as x + 0y + 0z = k, where k is a constant. This means that x can take on any value, and y and z are free variables. Therefore, there are infinitely many solutions to the system.

In summary, the RREF of a singular matrix can provide information about the existence and nature of solutions to the corresponding system of equations. It is important to carefully analyze the RREF in order to determine if the system has no solution or an infinite number of solutions.

A singular system is a system of equations where there is no unique solution. This means that there are either infinitely many solutions or no solutions at all.

A system is singular if the determinant of its coefficient matrix is equal to zero. This means that the system has either no solutions or infinitely many solutions.

Yes, a singular system can have infinitely many solutions. This occurs when the equations in the system are not independent and are essentially describing the same relationship.

A singular system has either infinitely many solutions or no solutions, while a system with no solution has no solutions at all. In other words, a singular system has some sort of solution, while a system with no solution has no solution at all.

A singular system cannot be solved using traditional methods, such as substitution or elimination. Instead, it can be solved by finding the general solution, which represents all possible solutions for the system. This can be done by setting one variable as a parameter and expressing the other variables in terms of that parameter.

- Replies
- 15

- Views
- 1K

- Replies
- 3

- Views
- 1K

- Replies
- 4

- Views
- 2K

- Replies
- 2

- Views
- 1K

- Replies
- 1

- Views
- 995

- Replies
- 2

- Views
- 2K

- Replies
- 1

- Views
- 877

- Replies
- 2

- Views
- 1K

- Replies
- 1

- Views
- 1K

- Replies
- 2

- Views
- 2K

Share: