Question

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.

Answer #1

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.

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.

f is a transformation of the plane so that
f(x,y)=(a⋅x+b⋅y,c⋅x+d⋅y) for some symmetric matrix M=[[a,b],[c,d]].
It is known that f(1,1)=(10,0) and f(8,1)=(52,28). Find the matrix
M.

(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...

. 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 =...

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 )

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 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) Find the standard matrix for the plane linear operator T
which rotates every point 60 degrees around the origin
(b) use the matrix to compute T(2,-8)

find a 4×4 matrix B such that the linear transformation x⇝Bx
preserves distance but does not preserve orientation

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