Question

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.

Answer #1

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.

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...

(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...

Complete translations: start at (1,3). reflect across y-axis,
rotate counter clockwise 90 degrees, translate (x+2),(y-1), rotate
180 degrees, reflect across x-axis, reflect across y-axis,
translate (x-1) (y+2), rotate 270 degrees clockwise, translate
(x+3)(y+1), reflect across the origin. connect all of your
points

(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...

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.

b) More generally, find the matrix of the linear transformation
T : R3 → R3 which is u1
orthogonal projection onto the line spanu2. Find the matrix of T.
Prove that u3
T ◦ T = T and prove that T is not invertible.

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 .

Find the matrix of the reflection of R2 across the line y =x/3
followed by the reflection of R2 across the line y = x/2 What type
of transformation of the plane is this composition?
thank you.

1.1. Let R be the counterclockwise rotation by 90 degrees.
Vectors r1=[3,3] and r2=[−2,3] are not perpendicular. The inverse U
of the matrix M=[r1,r2] has columns perpendicular to r2 and r1, so
it must be of the form U=[x⋅R(r2),y⋅R(r1)]^T for some scalars x and
y. Find y^−1.
1.2. Vectors r1=[1,1] and r2=[−5,5] are perpendicular. The
inverse U of the matrix M=[r1,r2] has columns perpendicular to r2
and r1, so it must be of the form U=[x⋅r1,y⋅r2]^T for some scalars
x...

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