Question

Using homogenous coordinates give the transformation matrix to scale by a factor of 2 in the x direction and 1.5 in the y direction.

Answer #1

Hey there!!

Here is the answer

Sx and Sy are the scaling factors in x and y-direction respectively.

The explanation is provided in the text only

if you have any doubts please leave them in the comments I will reply asap

Please do upvote if you like the answer

Thanks for asking!!

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.

1. A tetrahedron originally has coordinates given in the table
below. Assume the tetrahedron is to be rotated 90 deg. about the
x-axis (positive rotation) such that point 1 remains fixed. Compute
the combined transformation matrix that performs this operation.
Compute the new coordinates of points 1-4
Point 1 x=1.5, y=.20, z=1.5
Point 2 x=2.0, y=0, z=0
Point 3 x=1.0, y=0, z=0
Point 4 x=1.6, y=2.5, z=.80
2. For the tetrahedron of problem 1, compute the transformation
matrix that rotates...

Problem: Find the matrix which represents in
standard coordinates the transformation S:ℝ^2→ℝ^2 which shears
parallel to the line L=a^⊥, where a=(8,6) such that a gets
transformed into a+s, with s=(−6,8).
S = _____ _____
_____ _____

3. Find the linear transformation T : R2 → R2 described
geometrically by “first rotate coun- terclockwise by 60◦, then
reflect across the line y = x, then scale vectors by a factor of
5”. Is this linear transformation invertible? If so, find the
matrix of the inverse transformation.

3.) Find the linear transformation T : R2 to R2 described
geometrically by "first rotate counter-clockwise by 60 degrees,
then reflect across the line y = x, then scale vectors by a factor
of 5". Is this linear transformation invertible? If so, find the
matrix of the inverse transformation.

(a) Let T be any linear transformation from R2 to
R2 and v be any vector in R2 such that T(2v)
= T(3v) = 0. Determine whether the following is true or false, and
explain why: (i) v = 0, (ii) T(v) = 0.
(b) Find the matrix associated to the geometric transformation
on R2 that first reflects over the y-axis and then
contracts in the y-direction by a factor of 1/3 and expands in the
x direction by a...

Give a formula for the area element in the plane in rectangular
coordinates x and y. (Answer:
dx dy, or more properly |dx ∧
dy|; either is acceptable, as are dy dx
and |dy ∧ dx|.)
Give a formula for the area element in the plane in polar
coordinates r and θ.
Give a formula for the volume element in space in rectangular
coordinates x, y, and z. (Answer:
dx dy dz, or more properly |dx
∧ dy ∧ dz|;...

. 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 matrix A in the linear transformation y =
Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That
is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an
orthogonal matrix ?I any case,find the eigen values and eigen
vectors of A .

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 13 minutes ago

asked 19 minutes ago

asked 23 minutes ago

asked 24 minutes ago

asked 30 minutes ago

asked 30 minutes ago

asked 30 minutes ago

asked 30 minutes ago

asked 37 minutes ago

asked 39 minutes ago

asked 51 minutes ago