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Question 823700: I need help with this math problem. I have to make an augumented matrix to solve it and I have three equations.
1. 3x-y+z=4
2. x+2y+3z=10
3. 3x+2y-z=-12
I have already made the matrix, but I need help on how to get the three numbers that I need.
The answer choices are
A. (0,5,6)
B. (-1,2,9)
C. (-1,-2,5)
D. (0,-2,2)
Found 2 solutions by TimothyLamb, math-vortex:
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
3x - y + z = 4
x + 2y + 3z = 10
3x + 2y - z = -12
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copy and paste the above standard form linear equations in to this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
answer:
x= -1
y= -2
z= 5
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now for the augmented matrix:
3 -1 1 4
1 2 3 10
3 2 -1 -12
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as for solving the linear system from the augmented matrix, it involves performing a sequence of row operations on the matrix, which include:
1) interchange two rows
2) multiply a row by a constant
3) add a multiple of a row to another row
---
the aim of the row operations is to make the left 3x3 sub-matrix into the identity matrix.
---
having done so, the solution appears as the three remaining numbers in column 4
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by math-vortex(648)  (Show Source):
You can put this solution on YOUR website!
Hi, there--
3x -y + z = 4
x + 2y + 3z = 10
3x + 2y -z = -12
The augmented matrix for this system is
Here is a very helpful site for showing the row operations to solve a matrix. The calculator will solve the matrix and show you all the steps, or it will let you practice by choosing each row operation yourself. (Great learning tool!)
http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=roc
The correct answer is C. (-1, -2, 5).
Good luck!
Mrs. Figgy
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