# Give the ranks of both the matrix of coefficients and the augmented

Hey!
I was looking at some problems since I have a mid term tomorrow and dont get how to do this one perhaps someone can help!

http://img143.imageshack.us/img143/3452/16856739ys6.jpg [Broken]

I dont know if im doing this right but i went backwards and found the vector equation to look like

x = 1 + 3t - s
y = s
z = t

(x,y,z) = (1,0,0) + t(3,0,1) + s(-1,1,0)
[1 1 3 l 1]
[0 0 0 l 0]
[0 0 0 l 0]

do the rank of the augmented matrix is 1 and does that mean the rank of the coefficient matrix is also 1 ?

b) for b part should i just plug in that coordinate in the x,y,z vecotr form to solve for s, and t and hope for the same answer to show it is a solution

c) for c should i use the two vectors given from the vector equation s(-1,1,0) and t(3,0,1)

d) not sure how to find distance between two planes :S

CAN SOMEONE TELL ME IF IM COMPLETELY LOST?
and cross them to get the normal then use the point given to get the scalar equation

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