Linear Algebra

Download Category: - (92.08 KB)

This question tests your understanding of linear transformations; in
particular, it tests your ability to determine the matrix of a linear
transformation with respect to given bases and to find the kernel and image
of a linear transformation.

The function t : R3 -? R3 is given by the rule
(x, y, z) 0-? (y – z, x + z, x + y).

(a) Use Strategy 1.1 in Unit LA4 to show that t is a linear transformation.
(b) Write down the matrix of t with respect to the standard basis for R3.
(c) Determine the matrix of t with respect to the basis
{(1, 0, 0), (1, 1, 0), (0, 1, 1)} for the domain and the standard basis for
the codomain.
(d) Find the kernel of t, describe it geometrically and state its dimension.
(e) Find a basis for the image of t, state the dimension of the image and
describe the image geometrically.
(f) Let s be the linear transformation
s : P3 -? R3
a + bx + cx2 0-? (a + c, b, a + b + c).
Find the matrix of s and the matrix of t ? s with respect to the
standard basis for the domain P3 and the standard basis for the
codomain R3.

Write a Review

Get a fresh solution of this question. Ask it now to our experts.

Ask Your Question

We have verified professionals who are ready to answer your question.


Save Time and Money

We choose experts who can quickly answer your question and that suit your budget.


Get Your Answer

Your satisfaction is 100% guaranteed. You can keep on asking questions until you get the answer you need.