Answered: Let T: R - R° be a linear…

Let T: R - R° be a linear transformation such that T(1, 0, o) = (2, 4, -1), T(0, 1, 0) = (1, 3, -2), and T(0, 0, 1) = (0, 2, -2). Find the indicated image. T(2, -4, 1) T(2, -4, 1) =

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 23E: Let T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find...

See similar textbooks

Related questions

Q: Let the linear transformation T : R → R³ be such that T(-2, 1) 3 (-1, 2,0) and T(1,3) %3 Т(0, —3,…

Q: Let T: R° - R° be a linear transformation such that T(1, 0, 0) = (-1, 2, 4), T(0, 1, 0) = (3, 1,…

A: Here we have to find out image of point (0,1,-3).

Q: Let T: R° → R° be a linear transformation such that T(1, 1, 1) = (2, 0, -1), T(0, –1, 2) = (-3, 2,…

Q: Let T: R-R be a linear transformation such that T(1, 0, 0) - (4, -1, 2), T(o, 1, 0) = (1, 3, -2),…

Q: Let T: R3 - R3 be a linear transformation such that T(1, 0, 0) = (4, -1, 2), T(0, 1, 0) = (1, -2,…

A: Given that T is the linear transformation such that T1,0,0=4,-1,2, T0,1,0=1,-2,3 and T0,0,1=2,-2,0.…

Q: Let T: R° → R° be a linear transformation such that T(1, o, 0) = (4, 2, -1), T(0, 1, 0) = (-2, 1,…

A: The solution is given as

Q: Which of the following is NOT a linear transformation? T:R? → R³, T x +y [x+2y. Or:R² -R°, T = 2x…

A: In the question we have to check which option is not having Linear Transformation.

Q: Find (a) the image of v and (b) the preimage of w for the linear transformation.T: R3→R3, T(v1, v2,…

Q: Determine if the given transformation is linear. Find the image of (1 2 3) T(x, y, z) = (x + 2y,3z –…

Q: If T : R → R´is a linear transformation such that 0F0000 4 -3 %3D then T II

Q: Find the bilinear transformation which maps the points z1=1,z2=i,z3=-1 into the points…

Q: Determine whether the linear transformation is invertible. If it is, finds its inverse. T(x,y,z,w)…

A: Consider the components of T(x,y,z,w) as a,b,c, and d and try to solve for x,y,z, and w.

Q: If T is a linear transformation and T(u), T(v), T(w) are linearly independent, then u, v, w are…

Q: Let T: R3 → R3 be a linear transformation such that T(1, 0, 0) = (4, –1, 2), T(0, 1, 0) = (1, –2,…

Q: Let T: R - R be a linear transformation such that T(1, 1, 1) (3, 0, -1), T(0, -1, 2) (-5, 4, -1),…

Q: b) Let L:R → R be a linear transformation such that 2 and L(k) =| 1 Find L(i) = 2, L(j) : 2

A: We will use the properties of linear transformations to solve this. We will begin by writing the…

Q: Let T: R → R be a linear transformation such that T(1, 0, 0) = (4, 2, –1), T(0, 1, 0) = (-2, 1, 3),…

Q: Let T: R° - R° be a linear transformation such that T(1, 0, 0) = (2, -1, 4), T(0, 1, 0) = (3, -2,…

Q: Find (a) the image of v and (b) the preimage of w for the linear transformation.T: R2→R2, T(v1, v2)…

Q: Let T: R3 → R3 be a linear transformation such that T(1, o, 0) = (4, –1, 2), T(0, 1, 0) = (1, 3,…

Q: Let T: R3 → R3 be a linear transformation such that T(1, 1, 1) = (5, 0, –1), T(0, –1, 2) = (-2, 4,…

Q: If T(0) = 0, then T is linear transformation. %3D

A: detailed solution is given below

Q: Let T: ²->² be a linear transformation that maps u = Use the fact that T is linear to find the image…

Q: Let T: R → R be a linear transformation such that T(1, 0, 0) = (-1, 4, 2), T(0, 1, 0) = (1, -2, 3),…

Q: (:) T 2, T = 2x +2, T = -I, 0 0 0 0 T 5x2. 1. ([::)-

A: T:M2×2→P2T1000=2, T0100=2x+x2, T0010=-x, T0001=5x2

Q: Let T: R3 → R be a linear transformation such that T(1, 1, 1) = (3, 0, -1), T(0, -1, 2) = (-2, 4,…

Q: Let T: R³ → R³ be a linear transformation such that T(1, 0, 0) = (4, -1, 2), 7(0, 1, 0) = (1, 3,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Determine whether the function is a linear transformation. T: R2 - R, T(x, y) = (3x2, 2xy, 3y2)…

A: This question is related to linear algebra.

Q: Let T : R3 R' be the linear transformation defined by Т(х, х2, хз) — (х1 — X2, Xә — Хз, Xз — X).…

A: A transformation is a general term for four specific ways to manipulate the shape and the position…

Q: Show that the transformation Ø : R2 → R³ defined by Ø(x,y) = (x- y,x+y,y) is a linear transformation

A: Given: A linear transformation ∅:R2→R3Such that ∅x,y=x-y,x+y,y

Q: Determine whether the function is a linear transformation. T: R2 - R°, T(x, y) = (/x, 2xy, Vy) O…

Q: Let T: R - R be a linear transformation such that T(1, 1, 1) = (2, 0, – 1), T(0, –1, 2) = (-5, 3,…

A: Linear Transformation : Let T : U→ V be an linear transformation . where, U and V be two vector…

Q: Let T: R3 - R3 be a linear transformation such that T(1, 1, 1) = (5, 0, –1), T(0, -1, 2) = (-3, 3,…

A: Let's find.

Q: Let, T:R'→R';T(x,y,z)= (x – y,2x + 3y + 2z,x + y+2z) 1. Test whether the transformation T are linear…

A: Given T(x , y , z) = (x-y , 2x+3y+2z , x+y+2z) Any transformation T is linear if T(aX) =…

Q: Let T: R → R3 be a linear transformation such that T(1, 0, 0) = (4, 2, –1), T(0, 1, 0) = (3, 1, –2),…

Q: For the linear transformation T(r,y,z)= (r-z,y+z,x+y) ker(T)= nullity(T)= : and rank(T)=

Q: Let T: R - R3 be a linear transformation such that T(1, 0, 0) = (2, -1, 4), T(0, 1, 0) = (-2, 3, 1),…

Q: Let T: R3 → R³ be a linear transformation such that T(1, 1, 1) = (4, 0, –1), T(0, –1, 2) = (-4, 3,…

A: T:R3→R3 be a linear transformationT1,1,1=4,0,-1T0,-1,2=-4,3,1T1,0,1=0,1,1

Q: Let the linear transformation T : R → R³ be such that T(1, 1, 1) = (2, –1, 4), T(1, 1, 0) = (3,0, 1)…

Q: Show that the transformation Ø : R2 → R3 defined by Ø(x,y) = (x-y,x+y,y) is a linear transformation

A: The function is a linear transformation, since for all x1,y1,z1,x2,y2,z2∈ℝ3 and k scalar,…

Q: Suppose that T is a linear transformation, with T(u,) = T(u2) =:: Find T(2u, - 3u,).

A: From the definition of linear transformation we can solve this question.

Q: Let T: R? →R² be a linear transformation that first performs a horizontal shear that into e, - 2e,…

A: The given linear transformation is, T:ℝ2→ℝ2 Since given that T first performs horizontal shear and…

Q: Let, T : R' → R';T(x, y,z) = (x + y + z,2y + z,2y + 3z) 1. Test whether the transformation T is…

Q: Find a linear transformation T: R →R whose range is spanned by {(1, 2, 0, – 4), (2, 0, – 1, – 3)}

Q: Let T: R³ → R³ be a linear transformation such that T(1, 0, 0) = (4, −1, 2), T(0, 1, 0) = (1, 3,…

Q: (a) Let T: R? → R² be a linear transformation that first performs a horizontal shear that transforms…

A: By the definition of linear transformation we solve question b.

Q: Find (a) the image of v and (b) the preimage of w for the linear transformation.T: R2→R3, T(v1, v2)…

Q: Let T: R3 → R3 be a linear transformation such that T(1, 0, 0) = (4, 2, -1), T(0, 1, 0) = (3, 1,…

Q: Let T: R3 → R3 be a linear transformation such that T(1, 0, 0) = (2, -1, 4), T(0, 1, 0) = (3, 1,…

A: Given that T: R3-->R3 be a linear transformation such thta T(1,0,0)=(2,-1,4), T(0,1,0)=(3,1,-2)…

Q: Let T:R → R? be a linear transformation that maps u = (5,2) into (2,1) and v = (1,3) into (-1,3).…

Question

Please answer all and indicate where I will put the answer

Let T: R -
- R° be a linear transformation such that T(1, 0, 0) = (2, 4, -1), T(0, 1, 0) = (1, 3, -2), and T(0, 0, 1) = (0, 2, -2). Find the indicated image.
T(2, -4, 1)
T(2, -4, 1) =

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 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.
Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.
Let T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find T(1,4) and T(2,1).
In Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|
Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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)
For the linear transformation from Exercise 38, find a T(0,1,0,1,0), and b the preimage of (0,0,0), c the preimage of (1,1,2). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformation T:RnRmby T(v)=Av. Find the dimensions of Rnand Rm. A=[020201010112221]
For the linear transformation from Exercise 37, find a T(1,0,2,3), and b the preimage of (0,0,0). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRm by T(v)=Av. Find the dimensions of Rn and Rm. A=[012114500131]
A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.
For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the preimage of (0,0). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRm by T(v)=Av. Find the dimensions of Rn andRm. A=[0110]