Systems of Equations (matrices)

[madisonhope96]

What is the solution of the matrix equation? ​I'm so confused! Does anyone know how to solve this problem step by step?

 

[HallsofIvy]

What is the solution of the matrix equation? ​I'm so confused! Does anyone know how to solve this problem step by step?

There are any number of methods.
1) treat it as simultaneous equations, 5x- 2y= 2, 2x- y= -4.

2) Find the inverse of the matrix \(\displaystyle \begin{bmatrix}5 & -2 \\ 2 & -1 \end{bmatrix}\) and multiply both sides of the equation by that inverse matrix.

3) Write the "augmented matrix", \(\displaystyle \begin{bmatrix}5 & -2 & 2 \\ 2 & -1 & -4\end{bmatrix}\)
and "row reduce".

Have you learned any of those methods?

 

[mmm4444bot]

I would add Cramer's Rule, as another method. (It requires knowing how to calculate a matrix's determinant.)

 

[HallsofIvy]

I hate Cramer's rule!

 

[mmm4444bot]

I hate Cramer's rule!

Cramer's Rule ain't all that fun, I agree. This is why I programmed it into my TI-89 (for both 2d and 3d systems) a few years back. Using my program is fun. :cool:

PS: I probably should have stated in my first post that Cramer requires one to work out the determinant of three matrices.