Using Cramer's Rule to solve for x of a 3x3 matrix?

Question

Here's the problem:

-x + 2y - 3z = 0
2x + z = 0
3x - 4y + 4z = 2

Answer 1

ok well first thing to do is set these 3 equations up as a matrix..

-1 2 -3
2 0 1
3 -4 4

here is your matrix
now cramer's rule for a 3x3 matrix can be used
here is the general formula
ax +by+cz=j
dx + ey+fz=k
gx+ hy+iz= l

ina the matrix it's gonna be like this
a b c
d e f
g h i

now by cramers rule we set up the equation like this
matrix A which is the one above and the 1x3 matrix consisting of
i
j
k
multipiled by eachother will give you your answer matris in the form of
x
y
z
so we use kind of an algebra and set it up like this: find det of one of the matrix's divided by determinite of the other
x = j b c
k e f
l h i divided by another 3x3 matrix a b c
d e f
g h i

i'll do x for you by substituting and you can do the rest for y and z

x = determinite of 0 2 -3
0 0 1
2 -4 4
divided by the determinite of -1 2 -3
2 0 1
3 -4 4
I'm assuming you know how to find determinites so your answer for the value of x will be the det of the top over det of the bottom.... good luck

bah unfortunatly my matrix's didn't work well on yahoo's thing so you gotta line them up

Answer 2

it isn't the matrix even with the undeniable fact that it truly is a few thing! take the 1rst and the third eq 4x + 5y + z = 6 (mult by (-2)) x + 2y + 2z = 6 -8x - 10y - 2z = -12 x + 2y + 2z = 6 upload both eq -8x + x - 10y +2y - 2z + 2z = -6 -7x - 8y = -6 (a million) take the second one and the third eq 2x - y + 2z =11 x + 2y + 2z = 6 (MULT by (-a million) 2x - y + 2z =11 -x - 2y - 2z = -6 upload thw 2 eq 2x - x - y - 2y + 2z - 2z = 11 - 6 x - 3y = 5 (2) Now take (a million) & (2) -7x - 8y = -6 x - 3y = 5 (Mult by seven) -7x - 8y = -6 7x - 21y = 35 upload the eq. -8y - 21y = -6 + 35 - 29y = 29 y = -a million So, use y = -a million to (a million) or (2). enable's opt for x - 3y = 5 x - 3(-a million) = 5 x +3 = 5 x = 2 Now, use y = -a million & x = 2 to between the preliminary eq to discover z 4x + 5y +z = 6 4*2 +5*(-a million) + z = 6 8 - 5 + z = 6 z = 3

Answer 3

im not sure how to solve it mathematically, but i have this program in my calculator that says
x= .4
y= -1
z= -.8
hope that helps

Answer 4

dude cramer's rule fuc king sucks