Answered: Let T: R3 → R3 be a linear…

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

A: Here, the given linear transformation T is: T:ℝ3→ℝ3 such that T(1,0,0)=(-1,2,4), T(0,1,0)=(-2,1,3),…

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

Q: b) Let T: R2 R be the linear transformation for which T(1,1) = 3 and T(0,1) = -2. Find T(x1, x2)

Q: Let T be a linear transformation from R2 into R2 such that T(1, −1) = (2, −3) and T(0, 2) = (0, 8).…

A: Let T be a linear transformation from R2 into R2 such that T(1, −1) = (2, −3) and T(0, 2) = (0, 8).…

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

Q: Let T be a linear transformation from R2 into R2 such that T(1, 0) = (1, 1) and T(0, 1) = (-1, 1).…

A: Let us consider a linear transformation T: V→W and T(v1)=w1, T(v2)=w2 Then any element u in v can be…

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

A: Given

Q: Let T: R - R° be a linear transformation such that T(1, 0, o) = (2, 4, -1), T(0, 1, 0) = (1, 3, -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: let T: R3 → R be the linear transformation defined by T(x 1, x 2, x3) = (x 1 - x2 - X3, X1 + 3x, +…

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: If T(u + v) = T(u) +T(v), then T is a linear transformation.

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: 'ind the standard matrix of the linear transformation T : R² → R³ that satisfies T(1,1) = (2, 1, 0)…

A: Linear transformation and matrix

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

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

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: Let T be a linear transformation from R2 into R2 such that T(1, 0) = (1, 1) and T(0, 1) = (-1, 1).…

A: A Linear transformation T is a function from one vector space to another vector space that has the…

Q: Assume that T defines a linear transformation and use the given information to find the matrix of T.…

A: To find: Use the given information to find the the matrix of T

Q: What is the dimention of the kernel of the linear transformation defined by T: R² → R², T[a a_ b] =…

Q: Let T:R2-R3 be a linear transformation defined by T(x.y)-(4x+y.x-2y,.5y). Then the rank of T is:

A: NOTE: Refresh your page if you can't see any equations. .

Q: Let T be a linear transformation from R2 into R2 such that T(1, 0) = (1, 1) and T(0, 1) = (-1, 1),…

Q: Let T: R³ R³ be a linear transformation such that 7(1, 1, 1) = (2, 0, -1), 7(0, -1, 2) = (-5, 5,…

Q: Find a linear transformation T: R' →R whose range is spanned by {(1, 2, 0, - 4), (2, 0, – 1, – 3)}

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: If the linear transformation T: R2 → R is such that T(1, 0) = (2, 3, 1) and T(1, 1) = (3, 0, 2),…

A: question:

Q: Let f : R² → R² be the linear transformation defined by f(x) = х. B = {{-1,2) , (–2, 3)}, c =…

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

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: that

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: Determine the kernel and image, as well as their basis and dimension, for the linear transformation…

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: If T:R2 → R is a linear transformation with T and T then: T =

A: Answer

Q: let T: R² → R² be a linear transformation and T(1,0)=(1,-1) T(0,1)= (0,2) then [:] None 3 [-] 1 -3 5

Q: Let T : M2x2 (R) → M2x2 (R) be the linear transformation defined by "(: :)-( ) "). 2x z y - z+ w T…

A: The solution is given as follows :

Q: Let T be a linear transformation from R2 into R2 such that T(1, 2) = (1, 0) and T(−1, 1) = (0, 1).…

Q: Let T be the linear transformation defined by T(x, y) = (y - 4x, 8x - 3y, -5x - 6y, 7x). Find its…

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

Q: 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,…

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

A: Given that T(1,1,1)=(2,0,-1) T(0,-1,2)=(-3,2,-1)…

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

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

A: We will find out the required value using linearity property of linear transformation.

Q: Let T : R4 → R? be the linear transformation where N (T) = span{(1,0,0, 0), (0, 1, 0, 0)}. Is T…

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

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: snip

A: For a matrix, if any scalar is multiplied to the whole matrix, each term of the matrix is multiplied…

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

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
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 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).
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
In Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|
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 be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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}.
In Exercises 1-12, determine whether T is a linear transformation. T:FF defined by T(f)=f(x2)
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]
Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a the kernel of T and b the range of T. c Determine the rank and nullity of T.