Search results

1. Abstract Algebra - ideals and generators

Homework Statement a.) Let a=3-8i and b=2+3i. Find x,y ϵ Z[i] such that ax+by=1. b.) Show explicitly that the ideal I=(85,1+13i) \subseteq Z[i] is principle by exhibiting a generator. Homework Equations Given ideal: I=(85,1+13i) \subseteq Z[i] a=3-8i b=2+3i Honestly, I am beyond lost...
2. Tangent plane question

I'm completely lost on this question, and it's due tomorrow morning. Help? Homework Statement What point on y=x2+z2 is the tangent plane parallel to the plane x+2y+3z=1? Homework Equations y=x2+z2 x+2y+3z=1 The Attempt at a Solution I have no idea what to do... Thanks!
3. Linear independence?

How do you know when a matrix (or equivocally a system of equations) is linearly independent? How do you know that it's linearly dependent? For example, given this matrix, [ 1 1 2 1] [-2 1 4 0] [ 0 3 2 2] How do we know if this matrix is linearly independent or dependent...
4. Free variables in linear algebra?

My questions is short and to the point: What exactly is a free variable (in a matrix, for example). How do you know if a variable is free? Here's a matrix that (apparently) has a free variable: [1 4 -3 0 0] [-2 -7 5 1 0 ] [-4 -5 7 5 0 ] Row reducing the matrix we end up with: [1 4 -3 0 0...
5. Question about solving augmented matrices and row operations

So I just started my Linear Algebra course yesterday. I am confused on one aspect. When asked to solve an augmented matrix, the teacher would employ row operations. I understand how the row operations lead from one matrix to the next, but what I don't understand is how we formulate which row...
6. Calculus III or Linear Algebra? Which one should I take first?

Firstly, as you may see, I'm a newbie to this forum so I apologize if I posted this question in the wrong place or violated any rules within this post. :) I have no idea as to which to take first. The course description for Linear Algebra says that "Calculus III is recommended but no...
7. Calculus III or linear Algebra? Which one should I take first?

Firstly, as you may see, I'm a newbie to this forum so I apologize if I posted this question in the wrong place or violated any rules within this post. :) I have no idea as to which to take first. The course description for Linear Algebra says that "Calculus III is recommended but no required"...