Question

Find the solution to the system of equations represented by the matrix shown below.

3 -1 7|53
1 7 1|61
9 1 1|67

A.x = 6, y = 21, z = 54

B.x = 6, y = 7, z = 6

C.x = 42, y = 7, z = 6

D.x = 54, y = 21, z = 54

Answer 1

Are you just checking answers, or are you not sure how to find it?

Answer 2

Both.

Answer 3

Well how can you check your answer and not know how to do it? You'd have no answer to check ;p

Answer 4

You don't know how to use gauss-jordan elimination to write a matrix in reduced row echelon form to retrieve the solution to a system of linear equations?

You can try plugging in values from each multiple choice answer until they fit.

Answer 5

True, you could find it by process of elimination certainly.

Answer 6

I was never taught how to do it. Its part of a test im taking..

Answer 7

That sucks :-(

Lets teach you :-D there are video tutorials out there I'll link one to you or I can type the algorithm here.

Answer 8

Okaay, thank you so much!

Answer 9

http://www.youtube.com/watch?v=CsTOUbeMPUo

Answer 10

ughh. this is so confusing :(

Answer 11

This matrix is a little difficult to do by hand.
if you see hard matrices like this in multiple choice you should probably guess it to get choice b (by trying all answers to see if they work). It is faster than elimination

To eliminate matrices you follow basic steps to eliminate each column:
1. switch a row containing a leading '1' into the top
2. perform row operations (multiplying row 1 and subtracting row 1 from the values in the other rows) to make all the other elements in the first column 0
3. switch columns and do the same steps but for the second row to have a leading 1

for this particular matrix you can follow these steps:

Eliminating the first column
1. switch rows 2 and 1 (so the top row reads 1 7 1 61)
2. multiply row 1 by 3 and subtract row 2 by row 1 (so row 2 reads 0 -22 4 -98)
3. multiply row 1 by 9 and subtract row 3 by row 1 (so row 3 reads 0 -62 -8 -410)

now you have a matrix that reads
[ 1 7 1 | 61 ]
[ 0 -22 4 | -98 ]
[ 0 -62 -8| -410]

next step is to do something like divide row 2 by -22, and then subtract it from row 3 (after multiplying by -62).


you should finally get something like

1 0 0 6
0 1 0 7
0 0 1 6

in the end