Hi, I have two problems from a precalculus worksheet that reallyhave me stumped.

Question

Hi, I have two problems from a precalculus worksheet that reallyhave me stumped. the teacher only wants the problems solvedsolved certain ways, which i do not know how to do correctly.
#1: find the inverse using row operations (i found the inverse, butnot by roe ops, and she'll take off points)
original matrix:
[-2 1 -1
0   2   0
4   3   3]
inverse:
[-3/2 3/2 1/2
    0    1/2    0
    2    -5/2   1]
can you show me how to do the row ops?

#2: solve the following using a full identity matrix (rowoperations to get identity matrix)
original equations:
9a-3b+c=7
4a-2b+c=1
a+b+c=7
i know the ans is 2, 4, 1, but i do not know how to show it by rowoperations/identity matrix

Please help! very important!

Explanation / Answer

1) I think you set it up like this: [-2 1 -1 1 0 0] [0 2 0 0 1 0] [4 3 3 0 0 1]
Do row operations until the identity matrix is on the leftside (split the 3x6 down the middle) and then the right side willmagically be the inverse!
2) Well row-operations seems pretty basic. I'll at leastset it up for you. [9 -3 1 7] [4 -2 1 1] [1 1 1 7]
Treat this as a 3 by 4 matrix and do row operations until the3x3 on the left is the identity. Once you get the identityit's basically a = value(1,4), b = value(2,4), c = value(3,4) ((((In other words, the answers are in the fourth column))))
BTW, I used to keep a dotted line in between the 3rd and 4thcolumns to remind myself that the fourth column is for theanswers.

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