Question

Consider the linear transformation T : R² ? R², given by reflection in the line y = -3x. a) Find the matrix representation, A_T of this transformation. SHOW THE DETAILS. b) What are the images of the following points under this transformation: i) (1, 2) ii) (-2, 2) iii) (0, 0) iv) (-2, 6) Please give your solutions in the form of a fraction times a vector whose components are integers, with no common factors. Answer only c) Is this transformation onto? d) Is this transformation one-to-one? e) Find the solution set to the equation: T(x) = x equivalently A_Tx = x. Hint - you can do a calculation OR just think about it. Question 4 - 12 marks Consider the linear transformation T : R³ ? R³, given by projection onto the plane 2x – 5y + 6z = 0. a) State a normal vector to this plane. b) Find the matrix representation, A_T of this transformation. SHOW THE DETAILS. c) What are the images of the following points under this transformation:

          Consider the linear transformation T : R² ? R²,
given by reflection in the line y = -3x.
a) Find the matrix representation, A_T of this transformation. SHOW THE
DETAILS.
b) What are the images of the following points under this transformation:
i) (1, 2) ii) (-2, 2) iii) (0, 0) iv) (-2, 6)
Please give your solutions in the form of a fraction times a vector
whose components are integers, with no common factors. Answer only
c) Is this transformation onto?
d) Is this transformation one-to-one?
e) Find the solution set to the equation: T(x) = x
equivalently A_Tx = x.
Hint - you can do a calculation OR just think about it.
Question 4 - 12 marks
Consider the linear transformation T : R³ ? R³,
given by projection onto the plane 2x – 5y + 6z = 0.
a) State a normal vector to this plane.
b) Find the matrix representation, A_T of this transformation. SHOW THE
DETAILS.
c) What are the images of the following points under this transformation:

$Consider the linear transformation T : R² ? R², given by reflection in the line y = -3x. a) Find the matrix representation, AT of this transformation. SHOW THE DETAILS. b) What are the images of the following points under this transformation: i) (1, 2) ii) (-2, 2) iii) (0, 0) iv) (-2, 6) Please give your solutions in the form of a fraction times a vector whose components are integers, with no common factors. Answer only c) Is this transformation onto? d) Is this transformation one-to-one? e) Find the solution set to the equation: T(x) = x equivalently ATx = x. Hint - you can do a calculation OR just think about it. Question 4 - 12 marks Consider the linear transformation T : R³ ? R³, given by projection onto the plane 2x – 5y + 6z = 0. a) State a normal vector to this plane. b) Find the matrix representation, AT of this transformation. SHOW THE DETAILS. c) What are the images of the following points under this transformation:$

Added by Ramon C.

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