Question

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.

Answer #1

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.

Let T be the function from R2 to R3 defined by T ( (x,y) ) = (x,
y, 0). Prove that T is a linear transformation, that it is 1-1, but
that it is not onto.

(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 → 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.

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...

(1) Consider the linear operator T : R2 ! R2 defined by
T
x
y
=
117x + 80y
??168x ?? 115y
:
Compute the eigenvalues of this operator, and an eigenvector for
each eigen-

(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...

10 Linear Transformations. Let V = R2 and W = R3. Define T: V →
W by T(x1, x2) = (x1 − x2, x1, x2). Find the matrix representation
of T using the standard bases in both V and W
11 Let T :R3 →R3 be a linear transformation such that T(1, 0, 0)
= (2, 4, −1), T(0, 1, 0) = (1, 3, −2), T(0, 0, 1) = (0, −2, 2).
Compute T(−2, 4, −1).

let let T : R^3 --> R^2 be a linear transformation defined by
T ( x, y , z) = ( x-2y -z , 2x + 4y - 2z) a give an example of two
elements in K ev( T ) and show that these sum i also an element of
K er( T)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 3 minutes ago

asked 3 minutes ago

asked 10 minutes ago

asked 13 minutes ago

asked 15 minutes ago

asked 17 minutes ago

asked 19 minutes ago

asked 21 minutes ago

asked 22 minutes ago

asked 22 minutes ago

asked 37 minutes ago