Linear Algebra (parametric representation) question

[thepillow]

I have an exam in linear algebra this week and I was reading a handout my professor gave us about representing hyperplanes non-parametrically and parametrically. I haven't been able to get in touch with him about the question I have, so I was hoping someone could give me some insight.

He gives this equation for a non-parametric representation of a hyperplane:

a₁x_{1 +} a₂x_{2 + ... +} a_nx_n = b


and then this equation for a parametric representation (with x_k = p_k):

x_n = b - (a₁/a_n)p1 + (a₂/a_n)p₂ + ... (a_n-1/a_n)p_n-1


My question is why are there + signs on the right side of the 2nd equation. It seems like we've subtracted the left side of the 1st equation (except the last term) from b and then divided by a_n. Shouldn't all the + signs in the 2nd equation be minuses (or at least there be parenthesis around everything after b - )? Is this just a typo or have I misunderstood something?

Thanks so much your help

 

[daon2]

It looks like a typo

 

[HallsofIvy]

It should be either \(\displaystyle x_1= b- (a_2/a_1)x_2- (a_3/a_1)x_3- \cdot\cdot\cdot- (a_n/a_1)x_n\)

or \(\displaystyle x_1= b- ((a_2/a_1)x_2+ (a_3/a_1)x_3+ \cdot\cdot\cdot+ (a_n/a_1)x_n)\).

 

[thepillow]

Ok, great. That's exactly what I thought but I wanted to double check.

Much appreciated.