Question

Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.

x – 5y + 2z = 0
x + 4y – z = 12
2x – y + 3z = 10

Answer 1

create an augrmented matrix and then use the gausian method to solve putting the matrix into reduced row echelon(rref) form

1 -5 2 0
1 4 -2 12
2 -1 3 10

simplifies to:

1 0 0 6.5
0 1 0 1.03
0 0 1 -0.66

therefore x = 6.5
y = 1.03
z = -.66

Answer 2

Method 1:
Create a 3x3 matrix of the coefficients and a 1x3 matrix of the RHS of each equation. Feed the results to the Mathematica function, LinearSolve and execute:\[\text{LinearSolve}\left[\left( \begin{array}{ccc} 1 & -5 & 2 \\ 1 & 4 & -1 \\ 2 & -1 & 3 \end{array} \right),\left( \begin{array}{c} 0 \\ 12 \\ 10 \end{array} \right)\right]=\{7,1,-1\} \]Method 2:
Form a comma separated list of the equations changing the equal sign
to double equal sign, to conform to the Mathematica syntax and feed the result to the function Solve:\[\text{Solve}[\{x-5 y+2 z==0,x+4 y-z==12,2 x-y+3 z==10\},\{x,y,z\}] \]=\[\{x\to 7,y\to 1,z\to -1\} \]That is how I would solve it.

Answer 3

@robtobey :-)

OK,

Double the first and add it to the second and triple it, add it to the third to get rid oz-> simultaneous,solve, substitute back....