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- Download: http://solutionzip.com/downloads/linear-algebra/
- 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.
- Download: http://solutionzip.com/downloads/linear-algebra/
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