What are the required steps for solving this matrix problem?

Question

1x + 1y + 5z = 9
2x + 3y + 9z = 17
-1x + 3y - 8z = -11

I got this far:

1 1 5 9
2 3 9 17
-1 3 -8 -11

Answer 1

You have A*n = b where
A = [[1 1 5],[2 3 9],[-1 3 -8]]
n = [[x],[y],[z]]
b = [[9],[17],[-11]]
To find n use:
n = A^-1 * b

Or if you are using a numerical routine the preferred way is:
n = A\b

If you are doing this by hand, row reduction of the augmented matrix would probably be your best bet.

Answer 2

Add row 1 to row 3 and replace row 3 with that so you get:

1 1 5 9
2 3 9 17
0 4 -3 -2

Now add -2 row 1 to row 2 and replace row 2

1 1 5 9
0 1 -1 -1
0 4 -3 -2

now add -4 row 2 to row 3 and replace row 3

1 1 5 9
0 1 -1 -1
0 0 1 2

so you see that z = 2

plugging that into row 2 we get

y - z = -1 so y - 2 = -1 and y = 1

then plug y and z into the 1st row to solve for x. Hope this helped.

Answer 3

There are many ways to proceed from this point. What method are you working on?

If you're trying to get an upper matrix, then you need to start performing row operations to make the lower terms zero.

1 1 5 9
0 1 -1 -1
0 4 -3 -2

1 1 5 9
0 1 -1 -1
0 0 1 2

So z = 2, y = 1, x = -2

Answer 4

Look at the 1st column. It is 1 2 -1
You want to make it 1 0 0
If you multiply the 3rd row by 2 and add it to the 2nd row and then use the result to replace the 2nd row , the first column will now be 1 0 -1
Now add the 1st row and 2nd row and use result to replace the 3rd row, , the 1st column now becomes 1 0 0 which is what you want.

Now turn your attention to the 2nd column. You want it to be
0 1 0. So do the necessary manipulations to achieve this. Then go to the third column and make it 0 0 1.

When you are finished, you will have a 3X3 martrix with the diagonal all ones and all other elements = 0

The 4th column will contain x y z, the solution set