Question

. In this question we will investigate a linear transformation F : R 2 → R...

. 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 = Rθ ◦ Hx ◦ R−θ for an appropriate choice of θ, and use this to calculate the standard matrix of F.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Can someone explain linear transformations which rotates vectors by certain degrees? Examples: R^3--> R^3: A linear...
Can someone explain linear transformations which rotates vectors by certain degrees? Examples: R^3--> R^3: A linear transformation which rotates vectors 90 degrees about the x axis/y axis/z-axis (how would the matrix look if about a different axis) what if it rotates 180 degrees? R^2-->R^2?
let let T : R^3 --> R^2 be a linear transformation defined by T ( x,...
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)
Find the standard matrix for the linear transformation f(a, b, c, d)=(b-c+d, 2b-3d). Find the standard...
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.
Find the matrix of the linear transformation which reflects every vector across the y-axis and then...
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.
(a) Let T be any linear transformation from R2 to R2 and v be any vector...
(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...
Let T be the linear transformation from R2 to R2, that rotates a vector clockwise by...
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...
We consider the plane region R delimited by the curves y = cos (x) and y...
We consider the plane region R delimited by the curves y = cos (x) and y = (x − π) ^ 2 −2. (a) Determine the volume of the solid generated by the rotation of R revolves around the right y = −3. (b) Determine the volume of the solid generated by the rotation of R revolves around the right x = 0. For (a) and (b), observe the following procedure: - Draw a sketch (2D) of the R region...
In this question we denote by P2(R) the set of functions {ax2 + bx + c...
In this question we denote by P2(R) the set of functions {ax2 + bx + c : a, b, c ∈ R}, which is a vector space under the usual addition and scalar multiplication of functions. Let p1, p2, p3 ∈ P2(R) be given by p1(x) = 1, p2(x) = x + 2x 2 , and p3(x) = αx + 4x 2 . a) Find the condition on α ∈ R that ensures that {p1, p2, p3} is a basis...
2.) Suppose we use a person's dad's height to predict how short or tall the person...
2.) Suppose we use a person's dad's height to predict how short or tall the person will be by building a regression model to investigate if a relationship exists between the two variables. Suppose the regression results are as follows: Least Squares Linear Regression of Height Predictor Variables Coefficient Std Error    T P Constant 20.2833 8.70520 2.33 0.0223 DadsHt 0.67499    0.12495 5.40 0.0002 R² 0.2673 Mean Square Error (MSE) 23.9235 Adjusted R² 0.2581    Standard Deviation    4.9000...
*Answer all questions using R-Script* Question 1 Using the built in CO2 data frame, which contains...
*Answer all questions using R-Script* Question 1 Using the built in CO2 data frame, which contains data from an experiment on the cold tolerance of Echinochloa crus-galli; find the following. a) Assign the uptake column in the dataframe to an object called "x" b) Calculate the range of x c) Calculate the 28th percentile of x d) Calculate the sample median of x e) Calculate the sample mean of x and assign it to an object called "xbar" f) Calculate...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT