Question

Find Eigenvalues and Eigenspaces for matrix:

The 2 × 2 matrix AT associated to the linear transformation T : R2 → R2 which rotates a vector π/4-radians then reflects it about the x-axis.

Answer #1

(12) (after 3.3)
(a) Find a linear transformation T : R2 → R2 such that T (x) =
Ax that reflects a
vector (x1, x2) about the x2-axis.
(b) Find a linear transformation S : R2 → R2 such that T(x) =
Bx that rotates a
vector (x1, x2) counterclockwise by 135 degrees.
(c) Find a linear transformation (with domain and codomain)
that has the effect
of first reflecting as in (a) and then rotating as in (b).
Give the...

Find the matrix of the linear transformation which reflects
every vector across the y-axis and then rotates every vector
through the angle π/3.

Find the standard matrix for the linear transformation f(a, b,
c, d)=(b-c+d, 2b-3d).
Find the standard matrix for the linear transformation that
flips the xy plane over the y axis and rotates it by π/4 radians
CCW.

(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...

Let T be the linear transformation from R2 to R2, that rotates a
vector clockwise by 60◦ about the origin, then reﬂects it about the
line y = x, and then reﬂects it about the x-axis.
a) Find the standard matrix of the linear transformation T.
b) Determine if the transformation T is invertible. Give detailed
explanation. If T is invertible, ﬁnd the standard matrix of the
inverse transformation T−1.
Please show all steps clearly so I can follow your...

Assume that T is a linear Transformation.
a) Find the Standard matrix of T is T: R2 -> R3 first rotate
point through (pie)/2 radian (counterclock-wise) and then reflects
points through the horizontal x-axis
b) Use part a to find the image of point (1,1) under the
transformation T
Please explain as much as possible. This was a past test
question that I got no points on. I'm study for the final and am
trying to understand past test questions.

Can
someone explain linear transformations which rotates vectors by
certain degrees?
Examples:
R^3--> R^3: A linear transformation which rotates vectors
90 degrees about the x axis/y axis/z-axis (how would the matrix
look if about a different axis)
what if it rotates 180 degrees?
R^2-->R^2?

Determine whether or not the transformation T is linear. If the
transformation is linear, find the associated representation matrix
(with respect to the standard basis).
(a) T ( x , y ) = ( y , x + 2 )
(b) T ( x , y ) = ( x + y , 0 )

LINEAR ALGEBRA
For the matrix B=
1 -4 7 -5
0 1 -4 3
2 -6 6 -4
Find all x in R^4 that are mapped into the zero vector by the
transformation Bx.
Does the vector:
1
0
2
belong to the range of T? If it does, what is the pre-image of
this vector?

. 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 =...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 16 minutes ago

asked 23 minutes ago

asked 39 minutes ago

asked 51 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago