Solving a systems of linear equations using a matrix

[AlexAmos]

Hello,

I am struggling to achieve with correct solutions to the following problems.
Any feedback or help would be greatly appreciated.

Regards,
Alex.

 

[Dr.Peterson]

Please show us what you tried, so we can see where you are struggling and help you with that.

In particular, we need to know what matrix methods you have learned, and then to see where you are going wrong.

You did read at least one of these, right?

• https://www.freemathhelp.com/forum/threads/guidelines-summary.112086/
• https://www.freemathhelp.com/forum/threads/complete-posting-guidelines-from-the-sites-owner.109846/

 

[HallsofIvy]

You titled this "using a matrix". Written in matrix form, Ax= B, that would be
$\displaystyle \begin{bmatrix}9 & a & 7 \\ 2 & 1 & b \\ 6 & 2 & 5 \end{bmatrix}\begin{bmatrix}x \\ y \\ z\end{bmatrix}= \begin{bmatrix}d \\ f \\ g \end{bmatrix}$. What methods have you learned for solving matrix equations? Do you know how to find the inverse of a matrix?

 

[Otis]

Hi Alex. One way is to write the augmented coefficient matrix corresponding to the given system, followed by transforming it into reduced row echelon form. If you're not sure what that means, check out the first video below. If it's familiar, then let us know where you're stuck. Otherwise, if you'd like to solve the matrix equation in post #3, you can check out the second video below, to see a worked example of finding the inverse of a 3×3 matrix.

[00:00-00:59] Reviews definitions of reduced row echelon form and row operations
[01:00-04:01] Worked example (system of two equations)
[04:02-10:00] Worked example (system of three equations)

Example of transforming a matrix into its inverse using row operations.

Does any of that stuff look familiar?

?