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Matrix ?

  • #1
solve eqautions using a matrix

x + y -z = 0
3x - y + z = 4
5x +z = 7

so i wrote the matrix

1 1 -1 0
3 -1 1 4
5 0 1 7

then i multiplied Row 1 by -3 and added that to row 2
and multiplied row 1 by -5 and added that to row 3
resulting in

1 1 -1 0
0 -4 4 4
0 -5 6 7

then i multiplied row 2 by - 1/4

1 1 -1 0
0 1 -1 -1
0 -5 6 7

then multiplied row 2 by 5 and added that to row 3

1 1 -1 0
0 1 -1 -1
0 0 1 2

now i subbed back in to eqns

x + y -z = 0
3x - y + z = 4
5x +z = 7

1x + 1y - 1z = 0
0x +1y - 1z = -1
0x + 0y + 1z = 2

so z = 2 and solving all the other equation i get x = 1 and y = 1
is this right because i tried solving these by subtraction and got somthing different
 
Last edited:

Answers and Replies

  • #2
neu
220
1
You have not constructed a matrix equation, you have just rewritten the coefficients in some kind of array/pattern

THe matrix equation is :

[tex]\begin{pmatrix}
1 & 1 & -1\\
3&-1 & 1\\
5&0&1
\end{pmatrix}
\begin{pmatrix}
x\\
y\\
z
\end{pmatrix}
=
\begin{pmatrix}
0\\
4\\
7
\end{pmatrix}

[/tex]
 
Last edited:
  • #3
308
0
The augmented matrix that 2slow to go fast used is correct.
All you need to do is plug x y and z back into your original equations and see if they make true statements.
Looks to me like they check out.
CC
 
  • #4
360
21
  • #5
i just got it i was substituting wrong thanks for the help
 

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