SOLUTION: hi! I haven't been successful in finding help online on how to do this type of problem, so any help is appreciated! thank you in advance! (the brackets are supposed to be connected

Question 1194065: hi! I haven't been successful in finding help online on how to do this type of problem, so any help is appreciated! thank you in advance! (the brackets are supposed to be connected to make two big brackets)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve the equation for x.
[2 3x -2]
det[0 -2 -2]=716
[6 5 x]
The solution set is{_}
Found 3 solutions by math_tutor2020, Solver92311, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Refer to this page
https://www.chilimath.com/lessons/advanced-algebra/determinant-3x3-matrix/
For a lesson on how 3x3 determinants work

Following the template mentioned on that page, we would have these steps:

This means
-40x-4 = 716
I'll let you take over to finish solving for x.

Tip:
You can use GeoGebra's CAS feature to verify the determinant is equal to -40x-4
CAS stands for Computer Algebra System
I typed this in for the input
Determinant({{2,3x,-2},{0,-2,-2},{6,5,x}})
You must be in the CAS mode or else the calculation won't work. This is due to the presence of the variable x.
See this link here
https://www.geogebra.org/calculator/gsdw7jqg
Once you determine the numeric value of x, you can switch back to regular calculator mode. Though you could stick to CAS as well.

Extra side note:
The determinant of the 2x2 matrix is

Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!

Solve for

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

To learn on how 3x3 determinants work, see the lessons
    - Determinant of a 3x3 matrix
    - Co-factoring the determinant of a 3x3 matrix
in this site.

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