be a basis
for R4 and let L : R4 -> R2
be a linear transformation such that
14. Let be a basis
for R4 and let L : R4 -> R2
be a linear transformation such that
What is the dimension of the kernel of L?
| A. 0 | B. 1 | C. 2 | D. 3 | E. 4 |
Solution The answer is C.
In this case we have, first,
Second, since
L maps R4 to R2, the dimension of the
range must be less than or equal to 2.
Third, L(e1)
and L(e2) are linearly independent, for one is not
a multiple of the other, so the dimension of the range space must
be at least 2.
Consequently,
the dimension of the range space is 2, and the dimension of the
kernel is 2.