Question

Create the homogeneous coordinate equivalent of a matrix that projects a point in R^2 onto the y=x line. Then use your new transformation on the point (-3,4).

Answer #1

Find a 3x3 matrix that performs the 2D transformation in
homogeneous coordinates:
a) Reflects across the y-axis and then translates up 4 and right
3.
b) Dilate so that every point is twice as far from the point
(-2,-1) in both the x direction and the y direction.

True or False
If A is the matrix of a projection onto a line L in R 2 and the
vector x in R 2 is not the zero vector, then the vector x − Ax is
perpendicular to the vector x.
If vectors u, v, x and y are vectors in R 7 such that u = 2v +
0x − 3y, then a basis for span(u, v, x, y) is {u, v, y}.

(a) Find the matrix of the reflection of R^2 across the line y =
(1 / 3)x followed by the reflection of R^2 across the line y =
(1/2) x. What type of transformation of the plane is this
composition?
b) Find the principal axes y1 and y2 diagonalizing the quadratic
form q = (x^2)1 + (8)x1x2 + (x^2)2

. In this question we will investigate a linear transformation F
: R 2 → R 2 which is defined by reflection in the line y = 2x. We
will find a standard matrix for this transformation by utilising
compositions of simpler linear transformations. Let Hx be the
linear transformation which reflects in the x axis, let Hy be
reflection in the y axis and let Rθ be (anticlockwise) rotation
through an angle of θ. (a) Explain why F =...

Find the x coordinate of the point, correct to two decimal
places, on the parabola y=6.17-x^2 at which the tangent line cuts
from the first quadrant the triangle with the smallest area.

A coin of diameter 1/2 is tossed randomly onto the plane
R^2.Find the probability p that the coin does not intersect any
line of the form:a)x=k, where k is an integer, b)x+y=k, where k is
an integer.

Problem 2. (20 pts.) show that T is a linear transformation by
finding a matrix that implements the mapping. Note that x1, x2, ...
are not vectors but are entries in vectors. (a) T(x1, x2, x3, x4) =
(0, x1 + x2, x2 + x3, x3 + x4) (b) T(x1, x2, x3, x4) = 2x1 + 3x3 −
4x4 (T : R 4 → R)
Problem 3. (20 pts.) Which of the following statements are true
about the transformation matrix...

Suppose f: R^2--->R is defined by f(x,y) = 3y. Is f
one-to-one? Is f onto? Is f a bijection?

How can we use the origin to locate a point (-2,-7) in the
coordinate plane?
A linear equation in two variables describes a relationship in
which the value of one of the variables."
Identify a slope and y-intercept: 3x+5-y=0

1. Find the polar co-ordinates of the point P whose
rectangular co-ordinates are (-3,4)
2. A curve has a polar equation r(1-sinθ)=2. Find its Cartesian
equation in the form y=f(x)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 34 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago