Math
posted by Lynn .
I cannot come up with the right answers for my matrix.
I need to write as a system of equation and solve the system.
1 2 3 x 1
1 1 1 y = 12
1 1 2 z 2
The answers I come up with are
31
15
15
when I check these, they will not work, what I am doing wrong?

1 2 3 1
1 1 1 12
1 1 2 2
I want the first column to be 1 0 0 so subtract second from first and add third to first
1 2 3 1
0 1 2 11
0 3 5 3
I want the second column to be 0 1 0 so
subtract twice the second from the first and subtract 3 times the second from the third
1 0 1 23
0 1 2 11
0 0 1 36
I want the third column to be 0 0 1 so multiply the third row by 1 first
1 0 1 23
0 1 2 11
0 0 1 36
now add the third to the first and subtract twice the third from the second
1 0 0 13
0 1 0 61
0 0 1 36
so I get x = 13 , y = 61, z = 36 
when I am adding and subtracting I mean rows by the way.

The idea is that I can add anything times and row to any other row, just as I can add anything times any equation to any other equation. In fact that is exactly what I am doing.
I select what I want to multiply each by to get an identity matrix on the left, column by column, thereby separating the variables. I am really solving the equations by elimination, just in a particular fashion. 
Oh, to write as a system of equations, multiply the coefficient matrix by the variable column
1 2 3 x 1
1 1 1 y = 12
1 1 2 z 2
means
1 x + 2 y + 3 z = 1
1 x + 1 y + 1 z = 12
1 x + 1 y + 2 z = 2 
Oh, the particular fashion is often called GaussJordan reduction
Respond to this Question
Similar Questions

Augmented Matrix
Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent. DO ALL WORK BY HAND. x + 2y + 4z = 6 y + z = 1 x + 3y + 5z =10 If one subtracts the first … 
Algebra 2(check pt 4)
1)Cramer's Rule is used to solve the system of equations:3m5n=12,4m+7n=5 Which determinant represents the numerator for n? 
Algebra II
1. solve this system using matrices: 3.7x2.3+4.2z=8 2.6+4.6y3.9z=10 8x+2z=20 2. Write this system as a matrix equation: 2x+y=8 7x3y=10 
math
Solve following system of equations? x+3z=2 2x+2y+z=4 3x+y2z=5 i need help with few so i can get hang of this math plz. Perform row operations write new matrix [132 312 211 073] R1+R2 using x,yand z variables write system linear 
Discrete Math
I am really stuck on these problems. I've worked a lot of them but I can't get these. Sometimes I think I know the answer but I can't show how I got it. 1.) Solve each matrix equation for X. 2X + 5A = B 2.) Find the following matrices: … 
Algebra help!
Please help and I would appreciate an explanation as to how you got to the answer. 1.) Solve the system by triangularizing the augmented matrix and using back substitution. 0.09x0.15y+0.39 0.18x+0.35y=0.88 2.) Solve the system by … 
Algebra help!
1.) Solve the system by triangularizing the augmented matrix and using back substitution. xy+z=1 xy4z=7 4x+y+z=6 2.) Perform the indicated row operation, then write the new matrix. 4 4  4 9 6  5 2R1+ R2 > R2 3.) Solve … 
Algebra multiple choice!
I have a few questions I need help with! Please explain if my answer was not right how you got to it. I got 1.) B 2.) A 3.) C 1. Solve the system by triangularizing the augmented matrix and using back substitution. If the system is … 
Math Check
Hi! Can someone check this for me? My teacher wants me to write the system of equations that will correspond to the final matrix. I have the matrix already, but I need help with the writing the system stuff. Thanks! Matrix: [10 2 
Math  system of eqns
Consider the system of equations: x1 + x2 + x3 = 6, −x1 − 2x2 + 3x3 = 1, 3x1 − 4x2 + 4x3 = 5. (a) Write down the augmented matrix for this system (b) Use elementary row operations to reduced the augmented matrix to …