solve this system by matrices
2x+3y-z=-8
x-y-z=-2
-4x+3y+z=6
Jessica, it would be quite cumbersome to attempt typing matrices in this format.
Do you know how to find the inverse of a matrix?
Find it then multiply it by the column vector
-8
-2
6
here is one method to find the inverse
http://www.purplemath.com/modules/mtrxinvr.htm
Personally I use a method using adjoints, which seems very easy to do once you do it a few times.
On the other hand it is not easy to explain.
Here is a page where they try, but the first part might seem confusing.
They also form the adjoint at the end, I form it as my first step
http://www.easycalculation.com/matrix/inverse-matrix-tutorial.php
To solve the system of equations using matrices, we can write the system in matrix form.
First, we need to represent the coefficients of the variables and the constants in the system of equations. Let's call this matrix A:
A = | 2 3 -1 |
| 1 -1 -1 |
|-4 3 1 |
Now, we need to represent the variables in a matrix, let's call it X:
X = | x |
| y |
| z |
Finally, we need to represent the constants in a matrix, let's call it B:
B = | -8 |
| -2 |
| 6 |
We can rewrite the system of equations in matrix form as:
AX = B
To solve for X, we can use matrix algebra. We multiply both sides of the equation by the inverse of matrix A:
(A^-1) * AX = (A^-1) * B
Since matrix A is square and non-singular (determinant is non-zero), it has an inverse.
To solve this system, you can use software or calculator that can perform matrix operations. Multiply both sides of the equation by the inverse of A, and then multiply the inverse of A with B to find the values of x, y, and z.