Hello Everyone,

I am currently working on this problem in Linear Algebra and I am starting to go crazy with it.

I have done my calculations over and over again, and I keep getting

the same answer that is not what Wolfram Alpha is getting when I double check my work.

I did double check on this problem by performing the regular determinant without reducing into echelon form, and I get the same answer as Wolfram, so I am wondering if I am doing the echleon form of this wrong.

I have to find the determinant by row reduction to echelon form.

So the matrix is:

[1 5 -3

3 -3 3

2 13 -7]

The first step I do is: 1/3R2->R2

[1 5 -3

1 -1 1

2 13 -7]

Next I take -1R1+R2->R2

[1 5 -3

0 -6 4

2 13 -7]

Then I take -2R1+R3->R3

[1 5 -3

0 -6 4

0 3 -1]

After that I 1/2R2->R2

[1 5 -3

0 -3 2

0 3 -1]

Then I R2+R3->R3

[1 5 -3

0 -3 2

0 0 1]

Now that I have my echelon form, I try to get my determinant:

det = 1[-3 2 - 5[0 2 -3[0 3

0 1] 0 1] 0 0]

Which makes my det = -3???

My other calculations and Wolfram are getting the answer as -18.

Could you let me know where I am going wrong with this problem? :(

Thanks!!