pre-cal help?

Question

i need help with doing metrix
the problem is
1 -1 2 3
-1 0 1 -2
3 2 1 4
-1 -2 0 -3

Answer 1

What are you trying to do the matrix? Find the inverse?

Is it a 4x4 matrix, or a 3x4 matrix with a 1x4 solution vector representing 4 equations in 3 variables?

My calculator says that the inverse should be:

−1/5 −1/6 +17/30 +2/3
−1/5 +1/3 +01/15 −1/3
+1/5 +1/2 +01/10 +0
+1/5 −1/6 +07/30 -1/3

Normally I'd work it out for you, but with numbers like that, it would look really crappy on here anyway.

Answer 2

You mean this is a matrix, and you want to reduce it? I'm going to assume it's a 4x4 matrix taken from 4 equations with 4 unknowns, all set to zero.

Add the first row to the second and fourth rows:

[1, -1, 2, 3]
[0, -1, 3, 1]
[3, 2, 1, 4]
[0, -3, 2, 0]

Multiply the first row by -3 (to get [-3, 3, -6, -9]) and add this to the second row:

[1, -1, 2, 3]
[0, -1, 3, 1]
[0, 5, -5, -5]
[0, -3, 2, 0]

We can simply the third row by dividing it by 5:

[1, -1, 2, 3]
[0, -1, 3, 1]
[0, 1, -1, -1]
[0, -3, 2, 0]

Now take the third row and add it to the first and second row. Then take the third row, multiply it by 3, and add this to the fourth row:

[1, 0, 1, 2]
[0, 0, 2, 0]
[0, 1, -1, -1]
[0, 0, -1, -3]

Divide the second row by 2. Add it to the third and fourth rows. Then multiply the second row by -1 (after already dividing by 2) and add it to the first:

[1, 0, 0, 2]
[0, 0, 1, 0]
[0, 1, 0, -1]
[0, 0, 0, -3]

Divide the last row by -3. Now add it to the third row, and add -2 times it to the first row. You get:

[1, 0, 0, 0]
[0, 0, 1, 0]
[0, 1, 0, 0]
[0, 0, 0, 1]

Swap the second and third rows, and you get the identity matrix. This shows that there's only ONE unique solution to the original set of 4 equations with 4 unknows, and that is the trivial solution (all variables = 0).

Answer 3

As it stands your matrix is over-determined, and can be broken down into (4) 3x3 matrices, each with its own solution set for a, b, and c. The solutions are not likely to be the same.
Otherwise the best you can do is find the determinant.
(0 + 4 + 24 + 0) - (-6 + 0 + 0 + 4) = 28 + 2 = 30