SOLUTION: how do i solve using inverse matrix method? x+2y-z=10 -2x+3y+z=6 3x-2y+2z=19

Algebra.Com
Question 624927: how do i solve using inverse matrix method? x+2y-z=10 -2x+3y+z=6 3x-2y+2z=19
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
First we write the system in matrix form:


Next we find the inverse of the coefficient matrix. One way to do this is to append the identity matrix:

and then use elementary row operations to, in effect, transfer the identity matrix to the front. Adding twice the first row to the second row and adding -3 times the first row to the third row:

Multiply row 2 by 1/7:

Add -2 times the second row to the first row and 8 times the second row to the third row:

Row 3 times 7/27:

At this point I gave up, mostly because the fractions were getting uglier and uglier. Fractions are not necessarily wrong. But most of the time problems are assigned where the fractions don't get too nasty. This led me to think that there was an error in either what you posted or in my work (even though I have checked it several times). Either way I did not think it worth much to either of us for me to continue.

So what I propose for you to do is this:
  1. Double check what you posted. Make sure everything is correct, especially the signs. If there was a mistake, then re-post the corrected problem.
  2. Double check the work I have done above. I think I have explained what I was doing at each step so you should be able to check my work. With a "fresh eye" you might be able to find an error I have not been able to find. If you do find an error in my work...
    1. Correct it.
    2. Re-do the steps from the error to where I left off.
    3. Continue from where I left off:
      1. Add appropriate multiples of the third row to each of the first two rows with the goal of turning the 3rd column in those two rows into zeros (like I used the first row to clear out the 1st column and the second row to clear out the 2nd column.
      2. The first three columns should now be the identity matrix. The last three columns will be the inverse of the coefficient matrix.
      3. Multiply the inverse matrix by the column matrix:

        in this order:
        inverse matrix * column matrix
        The result will be a column matrix of the same size. The elements of this matrix are the solutions for x, y and z (in that order).
I'm sorry I was unable to be of more help with this.
RELATED QUESTIONS

Solve the following system equation using inverse matrix. x + y + z = 2 3x + 2y – 2z... (answered by Edwin McCravy)
Using matrix inverse method sole linear equations- x+y+z=17 -2x+3y+5z=47... (answered by lynnlo)
Solve a system using the inverse of a 3x3 matrix. 6x-5y-z=31, -x+2y+z=-6,... (answered by Edwin McCravy)
Solve using addition method x+3y+z=6 3x+y-z=-2... (answered by Alan3354)
X+2y-3z=11 3x+2y+z=1 2x+y=1 1. solve this matrix using Gaussian method 2.... (answered by Alan3354)
Solve by using matrix method 2x-y+z=3 x+2y-z=3... (answered by stanbon)
Question no 04: Solve the following system of equations Using Inverse Matrix Method... (answered by math_helper)
5x-3y+7=11 3x+y-2z=11 -x+2y+z=11 Using the matrix method,which row of operations can i (answered by Fombitz)
Solve the systems using the inverse matrix method: 5. {-3x + 9y = 9 { 3x + 2y =... (answered by hkwu)