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    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...
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    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!
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    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...
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    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...
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    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...
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    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...
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    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"...
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