Question

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.

Answer #1

(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

* Consider the transformations T1=‘reflection across the x-axis’
and T2=‘reflection across the line y = x’. (a) Find the matrices A1
and A2 corresponding to T1 and T2, respectively. (b) Show that (A1)
2 = I, and give a geometrical interpretation of this. (c) Use
matrix multiplication to find the geometric effect of T1 followed
by T2, showing all your reasoning. (d) The product T (θ)T (φ) of
any two reflections T (θ) and T (φ) with angles θ and...

Let ? denotes the counterclockwise rotation through 60 degrees,
followed by reflection in the line ?=?.
(i) Show that ? is a linear transformation.
(ii) Write it as a composition of two linear
transformations.
(iii) Find the standard matrix of ?.

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.

Consider the transformation T: R2 -> R3 defined by
T(x,y) = (x-y,x+y,x+2y)
Answer the Following
a)Find the Standard Matrix A for the linear transformation
b)Find T([1
-2])
c) determine if c = [0 is in the range of the transformation
T
2
3]
Please explain as much as possible this is a test question that
I got no points on. Now studying for the final and trying to
understand past test questions.

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...

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 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.

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