Determine the kernel and range. HELP???
Determine the kernel and range of the transformation defined by the matrix
6 4
3 2
.
(Enter your answers as a comma-separated list. Enter each vector in the form
(x1, x2, ...).
Use r for any arbitrary scalar.)
Show that dim ker(T) + dim range(T) = dim domain(T).
dim ker(T) + dim range(T) = dim domain(T) right double arrow implies
Determine the kernel and range of the transformation defined by the matrix
6 4
3 2
.
(Enter your answers as a comma-separated list. Enter each vector in the form
(x1, x2, ...).
Use r for any arbitrary scalar.)
Show that dim ker(T) + dim range(T) = dim domain(T).
dim ker(T) + dim range(T) = dim domain(T) right double arrow implies
1 Answer
Explanation:
The transformation takes the vector
The range
It is easy to see that
It is easy to see that all the elements of
The Kernel
The kernel of the transformation is defined by
So, if
Which will be satisfied by
It is obvious that
Rank-nullity theorem
Since
Thus the rank-nullity theorem
is verified by