Covered today: (NOTE: this is not in the book) Linear transformations and
matrix representation of linear transformations.
For Next time:
1.
Determine if the following functions are linear transformations. Justify the
answer.
(a)
(b)
(c)
2.
Find a matrix that represents each of the following linear transformations:
(a)
(b)
(c)
(d)
3.
Find the dimension of the image of the linear transformations in (2) and the
dimension of the kernel.
4.
The matrix
produces a stretching in the x-direction. Draw the circle and sketch around
it the points that result from multiplication by . What shape is the curve?
5.
What matrix represent the transformation that
(a)
project every vector onto the xy-plane.
(b)
refect every vector through the xy-plane.
6.
We know that the derivative is a linear transformation. Find the
matrix that represents on the space of polynomials of degree 3. What is the
nullspace and the column space, and what do they mean in terms of polynomials.