course
I have almost finished all the sections but I am having a big problem finding the inverse of a matrix. Just one problem for example:35.
1 -1 1
0 -2 1
-2 -3 0
OK. Your augmented matrix would be
1 -1 1 1 0 0
0 -2 1 0 1 0
-2 -3 0 0 0 1
so far I have done this, and this is about the 3rd attempt:
add 1 to row 3
1 -1 1 1 0 0
0 -2 1 0 1 0
-1 -2 1 1 1 2
row 1 + row 3 of previous matrix would be -1 -4 1 1 0 1
add 1 to row 3
1 -1 1 1 - 1 1
0 -2 1 0 -2 1
0 -1 2 1 0 3
row 1 was
1 -1 1 1 0 0
Adding row 1 to row 3 won't change row 1 to 1 -1 1 1 - 1 1.
mult. row 3 by 1/3
1 - 1 1 1 -1 1
0 -2 1 0 -2 1
0 0 3 1 0 3
row 3 was
0 -1 2 1 0 3
1/3 of this would be
0 -1/3 2/3 1/3 0 1
mult. row 2 by (-1/2)
1 -1 1 1 - 1 1
0 -2 1 0 -2 1
0 0 1 1/3 0 1
R2 = -1R2+R1
1 - 1 1 1 -1 1
0 1 1 0 1 -1/2
0 0 1 1/3 0 1
multiply row 2 by (-1/2)
1 -1 1 1 -1 1
0 -2 0 1 -2 3/2
0 0 1 1/3 0 1
I have gotten this far after several attempts and have only 2 spots right, because the calculator tells me the answer is
3 -3 1
-2 2 -1
-4 5 -2
More than the solution to just this problem, I wanted to know whether there are any more specific steps to take. I have read the book and the notes and I seem to be taking the wrong approach because I can get most of the positions on the left to the right number, but the answer is still not right. I was able to get the 2x2's right, but I haven't been able to get a single 3x3 right."
Solution:
1 -1 1 1 0 0
0 -2 1 0 1 0
-2 -3 0 0 0 1
add 2 * row 1 to row 3
1 -1 1 1 0 0
0 -2 1 0 1 0
0 -5 2 2 0 1
take -1/2 of row 2
1 -1 1 1 0 0
0 1 -1/2 0 -1/2 0
0 -5 2 2 0 1
add 5 * row 2 to row 3
1 -1 1 1 0 0
0 1 -1/2 0 -1/2 0
0 0 -1/2 2 -5/2 1
multiply row 3 by -2
1 -1 1 1 0 0
0 1 -1/2 0 -1/2 0
0 0 1 -4 5 -2
add 1/2 of row 3 to row 2
1 -1 1 1 0 0
0 1 0 -2 2 -1
0 0 1 -4 5 -2
add row 2 to row 1, then subtract row 3 from the resulting row
1 0 0 3 -3 1
0 1 0 -2 2 -1
0 0 1 -4 5 -2
See all my notes, and let me know what you still do and do not understand about the process.