1. Find for the vector ν = (1,2,3) in R3 all vectors w that are ...

Question

1. Find for the vector ν = (1,2,3) in R3 all vectors w that are perpendicular to ν. That is, find a pair v1 and v2 of vectors such that any such w is a general superposition of v1 and v2.

2. Find an equation ax + by + cz of the plane in R3 which contains the origin (0, 0, 0) and the vectors (1, −1, 0) and (1, 1, 1).

3. Solve over the complex numbers
x + iy = 2
x − iy = 1

4. Create and solve the equation using Gaussian Elimination.

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