# Thread: MATRICES (cramer's rule) help needed

1. ## MATRICES (cramer's rule) help needed

MATRICES
Solve the following . ( Cramer's Rule )

Q) x+2y+3z=7
3x+4y+2z=9
2x+5y+4z=9

2. Originally Posted by raza9990
MATRICES
Solve the following . ( Cramer's Rule )

Q) x+2y+3z=7
3x+4y+2z=9
2x+5y+4z=9
What help do you want? You cite Cramer's rule. Do you know what that is?

Cramer's rule says that the solutions of a system of equations
$a_{11}x+ a_{12}y+ a_{13}z= b_1$
$a_{21}x+ a_{22}y+ a_{23}z= b_2$
$a_{31}x+ a_{32}y+ a_{33}z= b_3$

are given by
$x=\frac{\left|\begin{array}{ccc}b_1 & a_{12} & a_{13} \\ b_2 & a_{22} & a_{23} \\ b_3 & a_{32} & a_{33}\end{array}\right|}{\left|\begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}$

$y=\frac{\left|\begin{array}{ccc}a_{11} & b_2 & a_{13}\\ a_{21} & b_2 & a_{23}\\ a_{31} & b_3 & a_{33}\end{array}\right|}{\left|\begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}$

$z=\frac{\left|\begin{array}{ccc}a_{11} & a_{12} & b_1 \\ a_{21} & a_{22} & b_2 \\ a_{31} & a_{32} & b_3\end{array}\right|}{\left|\begin{array}{ccc}a_{ 11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}$

Put in the numbers for your equations and calculate the determinants. Have you done that yet?

3. Originally Posted by HallsofIvy
What help do you want? You cite Cramer's rule. Do you know what that is?

Cramer's rule says that the solutions of a system of equations
$a_{11}x+ a_{12}y+ a_{13}z= b_1$
$a_{21}x+ a_{22}y+ a_{23}z= b_2$
$a_{31}x+ a_{32}y+ a_{33}z= b_3$

are given by
$x=\frac{\left|\begin{array}{ccc}b_1 & a_{12} & a_{13} \\ b_2 & a_{22} & a_{23} \\ b_3 & a_{32} & a_{33}\end{array}\right|}{\left|\begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}$

$y=\frac{\left|\begin{array}{ccc}a_{11} & b_2 & a_{13}\\ a_{21} & b_2 & a_{23}\\ a_{31} & b_3 & a_{33}\end{array}\right|}{\left|\begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}$

$z=\frac{\left|\begin{array}{ccc}a_{11} & a_{12} & b_1 \\ a_{21} & a_{22} & b_2 \\ a_{31} & a_{32} & b_3\end{array}\right|}{\left|\begin{array}{ccc}a_{ 11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|}$

Put in the numbers for your equations and calculate the determinants. Have you done that yet?
plz can u solve it for me.
i cant figure it out

4. You've been given the complete set-up for applying Cramer's Rule. All that remains is the plug-in-chug, computing the numerical values of the determinants (perhaps in your calculator or other technology), and simplifying the resulting fractions.

Where are you stuck? Please be complete. Thank you!