Question

**Problem**: Find the matrix which represents in
standard coordinates the transformation S:ℝ^2→ℝ^2 which shears
parallel to the line L=a^⊥, where a=(8,6) such that a gets
transformed into a+s, with s=(−6,8).

S = _____ _____

_____ _____

Answer #1

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.

Problem 2. (20 pts.) show that T is a linear transformation by
finding a matrix that implements the mapping. Note that x1, x2, ...
are not vectors but are entries in vectors. (a) T(x1, x2, x3, x4) =
(0, x1 + x2, x2 + x3, x3 + x4) (b) T(x1, x2, x3, x4) = 2x1 + 3x3 −
4x4 (T : R 4 → R)
Problem 3. (20 pts.) Which of the following statements are true
about the transformation matrix...

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.

7.18) Find the matrix of the cross product transformation
Ca: R3-->R3 with respect to the
standard basis in the following cases:
1) a = e1
2) a = e1 + e2 +
e3

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.

. 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 =...

Problem 1: Which of the following equations represents a plane
which is parallel to the plane
36?−18?+12?=30
and which passes through the point (3,6,1) ?
a). 6?−3?+2?=3
b). 6?+3?−2?=34
c). 36?+18?−12?=204
d). 6?−3?+2?=2
e). 36?+18?+12?=228
Problem 2: At which point(s) does the helix r
(t)=〈cos??/4, sin??/4, ?〉 intersect the sphere ?2+?2+?2=5 ?
a). (0,1,2) and (0,−1,−2)
b). (−1,0,4) and (−1,0,−4)
c). (1,0,4) and (−1,0,−4)
d). (0,1,−1) and (0,1,1)
e). (0,1,−1) and (0,−1,1)

(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)

he figure below shows the payoff matrix for two firms, Firm 1
and Firm 2, selecting an advertising budget. For
each cell, the first coordinate represents Firm 1's payoff and the
second coordinate represents Firm 2's payoff. The firms
must choose between a high, medium, or low budget.
Payoff Matrix
Firm 1
High
Medium
Low
Firm 2
High
(0,0)
(5,5)
(15,10)
Medium
(5,5)
(10,10)
(5,15)
Low
(10,15)
(15,5)
(20,20)
Use the figure to answer the following questions. Note:
you only need...

Find the Laplace transform of the given function:
f(t)=(t-3)u2(t)-(t-2)u3(t),
where uc(t) denotes the Heaviside function, which is 0 for
t<c and 1 for t≥c.
Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).
L{f(t)}=
_________________ , s>0

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