MATRICES (cramer's rule) help needed

**raza9990** · November 13th 2009, 03:54 AM

MATRICES
Solve the following . ( Cramer's Rule )

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

**HallsofIvy** · November 13th 2009, 04:05 AM

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?

**raza9990** · November 13th 2009, 07:44 AM

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

**stapel** · November 13th 2009, 07:48 AM

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!

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