Did My Matrix Calculations Lead to the Correct Solution?

Subspaces have to satisfy certain properties such as being closed under addition and scalar multiplication. In summary, a subspace is a subset of a vector space that is also a vector space.
  • #1
elle
91
0
I've been asked to solve the following matrix and find the solutions but I'm not sure if I've reached the correct 'end' matrix.

Original matrix:

1 2 -1 3
-1 3 4 10
-1 1 -2 8

The last matrix I got after my calculations:

1 2 -1 3
0 1 1 11/3
0 0 8 26/3

:confused:

Thanks for reading
 
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  • #2
What do you mean by "solving" a matrix? I know how to solve equations and I know, more generally, how to solve problems but I don't know what is meant by solving a matrix.
You appear to be row-reducing a matrix to row-echelon form. If so that is certainly not what I get. How about stating exactly what the problem is and showing your work?
 
  • #3
oh its okay, I've managed to work out where I went wrong. Sorry for not stating the problem clearly :rolleyes:

Erm but I have two more questions to ask, and was wondering if anyone can offer me some help or hints. I haven't got any working for this because I really do not have any idea how to approach the answer.

Can anyone explain to me what a subspace is? I've got notes on it but I'm confused with all the notation etc. Thanks in advance!

http://tinypic.com/f1mp3b.jpg"
 
Last edited by a moderator:
  • #4
elle said:
...
Can anyone explain to me what a subspace is?
...
A subspace of a vector space is just a subset of the vectors in the space that are also a vector space. For example, R2 is a 2-dimensional vector space. The set of vectors (x,y) that satisfy the equation y=x is a subspace of R2 but the set of vectors (x,y) that satisfy x2 + y2 = 1 is not.
 

FAQ: Did My Matrix Calculations Lead to the Correct Solution?

How do I know if my matrix is solvable?

To determine if a matrix is solvable, you can use the determinant of the matrix. If the determinant is equal to zero, then the matrix is not solvable. If the determinant is non-zero, then the matrix is solvable.

What is the purpose of solving a matrix?

Solving a matrix allows you to find the values of variables that satisfy a system of equations. This is useful in various fields such as engineering, physics, and economics.

How do I solve a matrix using Gaussian elimination?

To solve a matrix using Gaussian elimination, you need to perform row operations to reduce the matrix to its reduced row-echelon form. This form will then reveal the values of the variables in the system of equations.

What do I do if I get confused at the end of solving a matrix?

If you get confused at the end of solving a matrix, it is important to double-check your calculations and make sure you have followed the correct steps. You can also seek help from a tutor or consult online resources for further clarification.

Can I use a calculator to solve a matrix?

Yes, you can use a calculator to solve a matrix. Most scientific calculators have a matrix function that allows you to input the matrix and perform row operations. However, it is important to understand the concepts and steps involved in solving a matrix manually before relying on a calculator.

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