Homework problem 3Consider the following.T(x, y) = (x + 3y, y)(a) Identify the transformation.O vertical contractionO horizontal expansionO vertical shearO vertical expansionOhorizontal shearO horizontal contraction(b) Graphically represent the transformation for an arbitrary vector in R².yT (x, y)y(x, y)(x, y)XT (x, y)T (x, y)yyT(x, y)(x, y)(x, y)X

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Answered: Homework problem 3 Consider the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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]Let ƒ : R → R³ be defined by f(x) = (−5x, 6x, 5x). Is ƒ a linear transformation? a. f(x + y) = -5x-5y, 6x+6y, 5x+5y f(x) + f(y) = -5x, 6x, 5x + -5y,6y, 5y Does f(x + y) = f(x) + f(y) for all x, y E R? Yes, they are equal b. f(cx) = -5cx, 6cx, 5cx c(f(x)) = C -5x, 6x, 5x Does f(cx) = c(f(x)) for all c, x ER? Yes, they are equal c. Is f a linear transformation? f is a linear transformation
Pls help ASAP. Pls show all work and calculations and pls dont miss any steps.
Please perform all the transformations step by step, thank you.
Justify if it is true: If:T → W a linear transformation, then Nuc(T) = T−¹({0})
Example 3 Determine the equation of a plane tangent to the surface defined by f(x, y) = √√x² + y2 at the point (3,4,5). x2 (a) Find a parameterization for the x = 3 trace of f. What is a direction vector for the line tangent to this trace at the point (3, 4, 5)? (b) Find a parameterization for the y = 4 trace of f. What is a direction vector for the line tangent to this trace at the point (3,4,5)? (c) The direction vectors in parts (a) and (b) form a plane containing the point (3,4,5). What is a normal vector for this plane? (d) Use your work in parts (a), (b), and (c) to determine an equation for the tangent plane.
2 Please answer all and indicate where I will put the answer
Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither. а. (х, у) — (2х, у+2) b. (х, у) — (2х, 2у) c. (x, y) → (x + 2, y + 2) d. (x, у) — (х — 2, у) Match the rule on the left with its correct description on the right.
Consider a constant vector B e R*. Is the (projection) function F(ā)=| a-B à - dot products – where äeR“ a linear transformation? Justify, always.
Consider the vectors i and i shown below, which are related by a reflection through the x-axis. y Suppose T: R' → R? is a linear transformation such that T(e1) = ei and T(7) = 2e1. Find T(w) or explain why it cannot be determined. Warning: The picture does not indicate any scale on the y-axis. That means we cannot estimate the y-components of these vectors j and w (aside from the fact that their y-components are clearly not zero)! 12
5.PS-16 Question Help A shoe store uses a 60% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $55? The selling price would be $ (Round to the nearest cent as needed.) Enter your answer in the answer box and then click Check Answer. All narte chowing Review progress Question 9. of 9 pe here to search
(c) Let C be the vector space of continuous real-valued functions on R. If T: C → C is defined so T(f(x)) = |ƒ (x)\, is T a linear transformation? Explain why or why not.
2) Which of the following are linear transformations from R2 - R2? (a) Shear: T(x, y) (x + cy,y) for some constantc T T()T() -C] T(cu) cT (u) u = (b) Translation: T(x, y) = (x + a, y + b) for some constants a and b (c) Blow-up: T(x, y) (ax, by) for some constants a and b (d) Rotation: if x = rcos0, y = rsin0, then T(x, y) (rcos(0 p), rsin(0 p)) for some constants angle p (e) Projection: given a fixed vector r = (a, b), T maps each point to the closest point on the line spanned by T |712 (f) Reflection: given a fixed vector r = (a, b), T maps each point to its reflection with respect to r 2x T ( = 2x,

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