Given: S = {(−1, 0, 1),(−1, 3, 7),(2, 3, 4)} ⊆ R^3 3. Show that there is no linear transformation L : R^3 → P_2 such that L(−1, 0, 1) = x + 1, L(−1, 3, 7) = x^2 − 2x and L(2, 3, 4) = x − 3.

Given: S = {(−1, 0, 1),(−1, 3, 7),(2, 3, 4)} ⊆ R^3 3. Show that there is no linear transformation L : R^3 → P_2 such that L(−1, 0, 1) = x + 1, L(−1, 3, 7) = x^2 − 2x and L(2, 3, 4) = x − 3.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 20CR: Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3....

See similar textbooks

Related questions

Q: 5, explain why lim = 1. e* =

Q: Consider the solid generated by revolving the region enclosed by y = √ a² −x² and y = 0 about the…

A: The solid is generated by revolving the region enclosed by y=a2-x2and y=0 about the x-axis. We have…

Q: One of the members of staff from the software organisation travels to Birmingham on a business trip.…

Q: OA. The maximum value is B. The maximum value does not exist. Select the correct choice below and,…

Q: n(n + 1) = 0 (mod 2) for any integer n 3n+ 1 = 0 (mod 2) for any integer n 7|999 37 | 999 365 = 1…

Q: X6n-2 = r X6n-2 = r n-2 2p+h p+h (2P II i=0 h n-2 2p+h II p+h i=0 (fei+sp + foi+7h) (fo1+39 +…

A: x6n-2=x6n-5+x6n-4x6n-5x6n-4+x6n-7 substitute the values…

Q: Determine the truth-value of the following statements if A and B are known to be true, and X and Y…

Q: Prove that S(n, 3) > 3 n−2 for all n ≥ 6, where S represents Stirling numbers. (Note:…

Q: Let A be a matrix given by 3-6 -1 4 -8 -2 -3 6 3 Find a 3x3 matrix B such that B 0 and AB = 0. A =

A: A=3-6-14-8-2-363 Finding the eigen value of the matrix A A-λI=3-λ-6-14-8-λ-2-36-λ3-λ…

Q: O 11 10 -9 -8 7 O O 65 -4 -3 2 (2, 10) (3,5) 3 (4, 2.5) ● (5, 1.25) 5 7 8 9 10 11 15 an = 20( - ) -…

Q: Problem 25 Consider the following heat Problem in dimunionless variables 0o Ц = Ихх - вх tro U…

A: Please check the equation and given solution.

Q: use Euler’s Midpoint Method with the time step indicated to approximate the given value of y(t)…

A: Given: y'=dydt=cosy+t ; y0=0, h=0.05 We have to find y(0.25) using Euler's Midpoint method.

Q: A tank initially holds 40 gallons of a brine solution containing lb of salt per gallon. At t = 0,…

A: We will form differential equation for amount of salt in the tank and then solve it to get amount…

Q: For each function f below, determine the range of f. Justify your answer in each case by describing…

A: To find the range of the function given below f(x,y)=2-2x2-y2

Q: 1. Find the dual of the given primal LP. Max Z = -2x1 -3x2 - 3x4 s. t. x1 + x2 + x4 = 5 -1/2 x1 +…

Q: 8.5 Using b = 2 and p = 8, find the two's-complement integer representation for a. 25 b. 127 C. -1…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: -6 -3 From the diagram above; -2 -1 4 2 0 -2 -8 1 2 3 ii. Identify two clear and distinct points on…

A: I have given the answer in the next step. Hope you understand that

Q: 2 4x 1 3 x2-4 dx

Q: B = [3 {[9][9]} 02 4 0 56

Q: 2. State the definition of a countable set we mentioned in the lecture and prove the following…

Q: Suppose G is a graph of order n ≥ 2. What is the minimum size of G, so that it is guaranteed to be…

Q: decide if the given statement is true or false,and give a brief justiﬁcation for your answer.If…

A: Symmetric matrix: A square matrix A of order n is said to be a symmetric matrix if and only if we…

Q: dR dt dF dt 2(1-7) ¹ R-RF -16F +4RF

Q: -8 -7 -6 15 the graph of a function f shown below. -4-3 17 AX -6- -8- 10+ 8- 4 -10- 6 2 C₂ 05 7 8…

A: We will use definition of concavity to identify where graph is concave up or down .

Q: Find the equation of the parabola described below. Find the two points that define the latus rectum,…

Q: 2. Carry out the following integrations by substitution only. 2.1 √3x(x² +1)² dx x² 2.2 √2x-1 3x4…

Q: Answer the following True or False: Let f(x, y) be differentiable at (zo, 30). Then the vector is a…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: - We intersect the surface z = y² - x² with the plane 3x + y = 0, the result is the curve r(t) = (t,…

Q: 3) Use FTC2 to find the following derivatives: a. b. d S [*cos(√2t) dt dx d dx >3 e5x tan ¹(√2t + 1)…

Q: I would want the steps to intergating the top equation to the bottom one

Q: 12. Which point represents the least value on the number line? A. Point V: - 3/1 C. Point T: 1 0 T 2…

Q: Determine the truth value of the following statements if A and B are known to be true, and X and Y…

A: As per the policy of bartleby the provisions is to solve only three sub parts of questions

Q: (a) Show that a solution to the equation above is u(t)= xet, where x and A are an eigenvector and…

A: A=3-221 Finding the characteristic equation of the matrix ∴A-λI=0⇒λ2-4λ+7⇒λ=4±16-282 =2±i3 The…

Q: 2. Solve the initial value problem dy dt (mana ty + y cost. with y(0) = 3, using the method of…

Q: You always enjoyed a Starbucks Iced Oat Latte every day (5 days a week) on your way to work at a…

A: (a) Total cost for one week = $5.70×5+$12.50×5+$20×3 = $151 Weekly savings = 151-10% of 151 =…

Q: What is the simplified form of Oy-4 y-6 Oy-4 y+6 Oy+4 y-6 Oy+4 y+6 y² + 7y+12 y²-3y-18 ?

Q: Verly that each of Umn (x14₁3) = e satisfies Laplace's equation Uxx+lay +lzz = 0 and the boundary…

Q: Find the minimum and maximum values of z = 2x + 3y, if possible, for the following set of…

A: Given, z=2x+3y, Subject to constraints x+y≤9-x+y≤3 2x-y≤12.

Q: Explain what type of nodes do we choose to avoid the Runge phenomenon?

A: To Explain: what type of nodes do we choose to avoid the Runge phenomenon?

Q: Prove that each of the following sequences diverges: (a) {4n - 5} (b) {√3n+ 1} 2n + 3 √n n² +7 8n +3…

Q: Problem 1. Find the poles and zeros of the following functions. Mark the finite poles with x and the…

A: Find zeroes and poles by putting numerator and deniminator zero.

Q: The function f(x) = 16(2)x represents the growth of a bee population every year in a remote swamp.…

Q: Which logarithmic graph can be used to approximate the value of y in the equation 2y = 3?

A: We have to solve given Questions.

Q: Problem. Substitution method is a frequently used technique in mathematics. Through an appropriate…

Q: Given the Fourier sine series of $(x) = x as show that the series can be integrated b) Find The…

Q: 1. Find the series solution to

Q: Let T : U → V be a linear transformation. 1. Let D ≤ V and consider the subset E = {u ∈ U | T(u) ∈…

Q: Compute the product AB by the definition of the product of matrices, where Ab, and Ab₂ are computed…

A: Guven that the matricesA=-23254-4 ,B=5-1-23

Q: 2. Which of the following series diverge by the BDT? (Σ(-2) k=0 ê (c) Σ Σ(1+1)" Σ(6) 13 (e) none of…

A: We have to check which series is divergent by basic divergent series test.

Q: Find general solutions of the systems in Problem Attached.

A: Given : x'=1001874-27-9-5x To Find : General solution of the system .

Question

Given: S = {(−1, 0, 1),(−1, 3, 7),(2, 3, 4)} ⊆ R^3

3. Show that there is no linear transformation L : R^3 → P_2 such that L(−1, 0, 1) = x + 1,
L(−1, 3, 7) = x^2 − 2x and L(2, 3, 4) = x − 3.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3. Find T(0,1,1)
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
The gray square in Table 1 has the following vertices: [00],[10],[11],[01] Apply each of the three transformations given in Table 1 to these vertices and sketch the result to verify that each transformation has the indicated effect. Use c=2 in the expansion matrix and c=1 in the shear matrix.
Is there a linear transformation T : R3 --> R2 such that T(1, 0. 3) = (1, 1)and T ( -2, 0, -6} = (2, 1)?
Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (2x, y).
Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (x, 6y).
If possible, give an example of a linear transformation T : IR3 → IR4 such that: Ker(T) = [(5, 0, 8 + 2), (−5, 5, 0)].
Find the linear fractional transformation that maps (1, 0, i) to (1, 0, 1+i).
Let L : R 2 → R 3 be defined by L(x, y) = (x − y, 0, x + y). Show that L is a linear transformation. What is the kernel of L? What is the nullity of and rank of L?
Find linear transformation whose kernel is spanned by S.
Please help with part b - how to show as simply as possible that T(\overrightarrow{x}) meets the two requirements (T(\overrightarrow{u}+\overrightarrow{v} and cT(overrightarrow{u}) = T(coverrightarrow{u}) and is a linear transformation
Show that the transformation defined as , is linear.