Cramer's Rule question

[markraz]

Hi I'm trying to understand this example of plane/plane intersection that uses Cramer's rule. The matrices in the denominator of the X and Y looks like a standard determinant of 2x2 matrix. However the numerator does not seem to fit into any of the standard 3x3 determinants I have outlined in orange. any ideas on which one I need to use?? or is this example using some variation?
Thanks in advance

 

[Steven G]

The determinants in the numerators are also 2x2. Do you see that? Do you know Cramer's rule? The determinants live up to Cramer's rule perfectly. Please explain why you think otherwise.

 

[markraz]

The determinants in the numerators are also 2x2. Do you see that? Do you know Cramer's rule? The determinants live up to Cramer's rule perfectly. Please explain why you think otherwise.

thanks for the reply, the reason why I am confused is the denominator shows a 2x2 where the numerator shows a 2 x 3. It just doesn't make sense to me. I don't see the pattern with the numerator, the denominator is obvious to me. I did a google search for 2x3 determinants and couldn't find anything.


thanks

 

[Steven G]

In solving for x, what would YOU replace the x column with for the determinant in the numerator?

Same question for solving for y.

Look more carefully at the size of the det in the numerator!!!!

 

[Steven G]

In your 1st post look at the two equation directly above with it says Cramer's rule in blue. What does it say after the two equal signs?????

 

[markraz]

In your 1st post look at the two equation directly above with it says Cramer's rule in blue. What does it say after the two equal signs?????

ok I think I get it now so based on this graphic. all makes sense

x=
e = 4 - t2
f = -3 + 4t
b = -1
d = 1

y=
a = 3
c = 2
e = 4 - t2
f = -3 + 4t




thanks for your help

 

[Steven G]

So you now see that the determinants in both numerators are 2x2, correct?

 

[markraz]

So you now see that the determinants in both numerators are 2x2, correct?

yes I finally see them, I appreciate your help, Thank you