Consider a nonzero vector in . Using a geometric argument, describe the kernel of the linear transformation from to given by,
See Definition A.9 in the Appendix.
The kernel is a line in space spanned by vector
The kernel of linear transformation is defined as follows:
The kernel of a linear transformation from to consists of all zeros of the transformation, i.e., the solutions of the equations .
It is denoted by ker or ker
The definition A.9 cross product in is given as follows:
The cross product of two vectors role="math" localid="1659527572946" and in is the vector in with three properties as follows:
We have given the linear transformation defined by ,
With the reference of definition in step 1, we have,
is any scalar, which means that the cross product is zero.
This implies that kernel is a line in space spanned by vector
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