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