Question

f:R^{2} to R^{2} is a linear transformation so
that f(1,4)=(10,11) and f(8,1)=(18,-36). Find the determinant of
the matrix of f.

Answer #1

1. f:R2 to R2 is a linear transformation so that f(1,2)=(16,4)
and f(8,1)=(38,-43). Find f(4,-2).
2. f:R2 to R2 is a linear transformation
so that f(1,4)=(32,15) and f(7,1)=(35,-3). Find the determinant of
the matrix of f.

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.

(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...

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.

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...

(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...

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.

. 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 =...

Consider the linear map ? : R2 → R2 which sends (1,0) ↦→
(−3,5) and (0,1) ↦→ (4, −1).
(a) What is the matrix of the transformation? What is the
change of coordinates matrix? Do they agree? How come? ( Please
compute both the matrix of the transformation and the change of
coordinates matrix!)
(b) Where does this transformation send the area between the
vector (4, 2) and the x-axis? Explain algebraically and draw a
picture.
(c) What is the...

Give an example of a linear transformation T:R2
-->R2 such that rank(T)=rank(T2) and T
does not equal T2. Write the matrix representation of
T(denoted [T]) with respect to the standard ordered basis

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