ropowiec2gkc
2022-04-03
Find a linear mapping G that maps to the parallelogram in the xy-plane spanned by the vectors and .
Lana Hamilton
Beginner2022-04-04Added 12 answers
Step 1
Given:
The maps to the parallelogram in the XY-plane spanned by the vectors and
Step 2
Here, basis vectors are . of UV-plane mapping linearly to S and T.
The mapping whereA,B, Cand D are constaint.
and
We have given the vectors in xy-plane.
That is
So, the liner mapping G that maps to the parallelogram in the XY-plane spanned by the vectors
and is
mhapo933its
Beginner2022-04-05Added 9 answers
Step 1
A simpler region in the uv-plane can be linearly mapped to a region described by two vectors r and s.
Step 2
r and s describe a parallelogram region.
Step 3
Recall how the basis vectors of the uv-plane map linearly tor and s. Write the vectors like this to see what is A, B, C, D:
Then write the mapping:
Step 4
It can be confirmed by checking the corners of the uv-rectangle :
Answer
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