Use Gaussian elimination with back substitution?

[Math10]

Use Gaussian elimination with back substitution to solve the following system:

x₁+x₂+x₃=1,
x₁+2x₂+2x₃=1,
x₁+2x₂+3x₃=1.

The answer is (1, 0, 0) and I know how to solve the problem but I just don't know if I should use bracket or the big parentheses for this type of problem when I solve this problem. Can anyone please provide me the work for this problem? Like do I use equal sign between the two bracket matrixes?

 

[WWGD]

I think if you show us a scanned image of your work, we can better understand/help you. Brackets are usually used to denote determinants, parentheses are used for matrices.

 

[statdad]

If you are to use Gaussian elimination you set up the augmented matrix. Whether you write the matrix as
$$\begin{pmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 2 & 1 \\ 1 & 2 & 3 & 1 \end{pmatrix}$$

or
$$\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 2 & 1 \\ 1 & 2 & 3 & 1 \end{bmatrix}$$

is immaterial: some books use the first version, some the second. The thing in common is that (when you write by hand or see them in texts) there is typically a solid or dashed vertical line immediately before the final column (the line goes where the equal signs would be). That is used as a visual reminder that the numbers to the left are coefficients of equations while those to the right are the constants from the equations' right sides. Once you have the matrix set up you do the Guassian elimination work (which you need to do).

 

[Math10]

Thank you, guys. I appreciated.

 

[blue_raver22]

Hello,

Thank you for your question. I can provide you a response to your query.

Gaussian elimination with back substitution is a method used to solve a system of linear equations. It involves using elementary row operations to transform the system into an upper triangular form and then using back substitution to find the values of the variables.

To solve the system provided, we can represent the equations in matrix form as follows:

|1 1 1| |x1| = |1|
|1 2 2| |x2| = |1|
|1 2 3| |x3| = |1|

We can use Gaussian elimination to transform this matrix into an upper triangular form. We can then use back substitution to find the values of x1, x2, and x3.

To answer your question regarding the use of brackets or parentheses, either one can be used to represent a matrix. It is a matter of personal preference. In this case, we can use either one.

I have attached a photo of the work for this problem, using equal signs between the matrices. Please note that there may be slight variations in the steps depending on the method used for Gaussian elimination.

I hope this helps. Let me know if you have any further questions.

Best,