Decide N(F) and V(F) for Linear mapping in basis w. Matrix
The matrix is
(1 2 ).
(3 6 )
Call it A
A 2 x 2 matrix its located in some basis
E = (e1,e2)
I want to find N(F) and V(F)
1. So I will start by findin N(F)
What does that mean?
Well
F(u) = zero vector
I want to know which vectors which will
Fall on the zero vector
This means it's the same as
AX=0
It would lead to a linear equation system
X1 + 2x2 = 0
3x1 + 6x2 = 0
So I suppose I should do gauss
If I eliminate 3x1 from row 2
I will get all of the 2nd row to become
0=0 if I multiplied row 1 with -3
Getting
0=0 leaves me wondering what to do next?
2. I guess V(F) is gotten by cross multiplying
Two column vectors of the matrix A
This also leaves me wondering because it's a
2x2 matrix
Could someone show me how to solve it?