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

For a system of 3 equations i would use elimination to break it down into a system of 2 equations w/ 2 variables, then use elimination again to reduce it to a single equation to solve for 1 variable. Then use substitution to find other 2 variables.

Answer 2

and is that it what is the answer

Answer 3

well to find the solution, you have to do the elimination method
pick 2 equations and eliminate a variable

Answer 4

whATS THE ANSWER

Answer 5

you asked for what method i would use, do you know the elimination method?

Answer 6

no?

Answer 7

Then how have you solved systems of 2 equations?

Answer 8

well i dont know have to answer the 2 last sentences

Answer 9

have you ever solved these type of problems before?
like
x + 2y = 4
-x - 3y = 6

Answer 10

I would use row reduction

Answer 11

um yes

Answer 12

\[\left[ \begin {array}{cccc} 1&-5&2&0\\ 1&4&-1&12
\\ 2&-1&3&10\end {array} \right] \to\left[ \begin {array}{cccc} 1&0&0&7\\ 0&1&0&1
\\ 0&0&1&-1\end {array} \right]
\]Unique solution:\[\begin{eqnarray*}
x &=& 7 \\
y &=& 1 \\
z &=& - 1 \\
\end{eqnarray*}\]

Answer 13

did you just answerd it

Answer 14

yes that is the solution, however i doubt matrix row operations are part of what you are learning in class, that is used in more advanced classes.
you need to learn how to do it using elimination or substitution methods first

Answer 15

okey

Answer 16

The beauty of applying linear algebra to systems of linear equations is that you can think of the coefficients of the system as a linear transformation.

The problem then boils down to, is there a vector x such that the image of the vector under the transformation is b or Ax = b. Since elementary row operations are null space preserving or (solution preserving), you can then get the matrix into a state where you can easily see if there is a unique solution (the transformation is one to one), a set of solutions, or no solutions (the case where b is not in the image of A).

Answer 17

yes
given Ax = B
x = A^-1*B
so if you have a graphing calculator, put in the coefficient matrices and find solution by entering " A^-1 * B"
what class is this for david?