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can u solve this problem and show the steps for me 2 understand............x+2y+z=-1
2x-y+z=1
x+y-2z=3 it has 2 b solved useing gaussian elimination
To do so, take the matrix of coefficients with the constants at the end of each row. What you have is
1 2 1 -1
2 -1 1 2
1 1 -2 3
The gaussian elimination converts the matrix to upper triangular at first. That is, multiply the first row by -2 and add to the second row. Multiply the first row by -1 and add to the third row.
In the second column, I believe you now have a -5 in row 2 and a
-1 in row three. Multiply row 2 by -1/5 and add that to the third row.
The third row says what z is.
Put this back into the second row which has a y and z in it (with coefficients). The value of y can be found.
Now that you have the values of y and z, put them into the first row and then you will have x and a coupke of constants. Once this has been done, the value of x can be found as well.
This is what is known as the backward substitution method. Using this, it can be seen that a matrix doesn't have to be solved. As a good check, however, put these values back in to the orginal matrix to make sure you're right.
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