Define a linear transformation T : R² → R³ byT(x1, x2) = (3x1 + x2, 5x1 + 7x2, 2x1 + 3x2)Find a matrix representation for T. If you are not sure about your answer, at least state the size ofthe matrix.

T:IR2→IR3T(x1,x2)=(3x1+x2,5x1+7x2,2x1+3x2)As T is from IR2 to IR3 thensize of matrix 3*2Basis for…

Define a linear transformation T : R² → R³ by T(x1, x2) = (3x1 + x2, 5x1 + 7x2, 2x1 + 3x2) %3D Find a matrix representation for T. If you are not sure about your answer, at least state the size of the matrix.

Define a linear transformation T : R² → R³ by T(x1, x2) = (3x1 + x2, 5x1 + 7x2, 2x1 + 3x2) %3D Find a matrix representation for T. If you are not sure about your answer, at least state the size of the matrix.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 1EQ: 1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .

See similar textbooks

Related questions

Q: find the standard matrix of the linear transformation in the given exercise

A: Given transformation is This can be written as

Q: Consider the transformation T: R² → R, Ti + x2 a) ъ) R? and R3 have their standard bases. Verify…

Q: Find a matrix A that induces the transformation T:ℝ3→ℝ2 given below. T[x y z] = 3x-3y+6z…

Q: Find the matrix A of the linear transformation from R to R' given by 5 T 6 x1 + -1 x2. %3D -8 7 A =

Q: Find the matrix M of the linear transformation T : R R? given by x1 2x1 – x2 + 4x3 T x2 -3x1 + 8x2…

Q: Determine whether T is a linear transformation. T: Mnn ---> Mnn defined by T(A) = AB -BA, where B…

Q: A linear transformation T : R* –→ R? whose matrix is -3 3 6 -2 2 3+ k is onto if and only if k +

Q: Determine whether the linear transformation represented by the matrix A is (a) one-to-one, (b) onto,…

Q: Find the standard matrix for the transformation T: Rª → R² defined by Wi = 2x1 + 3x2 – 5x3 – X4 w2 =…

Q: Consider the linear transformation T: R? → R³: X2 ((:)- X1 -5x1 + 13x2 -7x1 + 16x2 T X2 Write down…

A: The matrix representation of given transformation is given as follows :

Q: Determine the linear transformation T: R→ R? that has the given matrix 2 -1 5 A = 3 1 -2

Q: Let T: R3 → R³ be the linear transformation defined by (E)-F x1 - x2 X2 - x1 X3 (a) Find the…

Q: Define a linear transformation T : R? → R37: R - R' by T(a1, x2) = (3xı + a2, 5a1 + 7x2, 2a1 + 3x2)…

A: Given linear transformation t :ℝ2→ℝ3 deined by Tx1, x2 =3x1, x2+5x1, 7x2+2x1, 3x2.we have to find a…

Q: Determine whether the function involving the n x n matrix A is a linear transformation. T: Mn,n…

Q: Find the matrix M of the linear transformation T : R³ → R² given by - (E) 6x1+ x2+ (-5)æz 8x1+ 3x3 M…

Q: Consider the transformation T from R' to R" given by + 22 7 8 Is this transformation linear? If so,…

Q: Let T be the linear transformation defined by T(1, 2, 3, 4, 5) = − 8x₁ + 4x2 x3 +54 + 3x5. Its…

Q: If T: R2 → R is a linear transformation for which T and T -2 2 and A is the standard matrix for this…

Q: Let A be the matrix representing the linear transformation T : R2 → R² defined by 2 2 What is the…

A: The objective is to find det(A)

Q: Find the matrix M of the linear transformation T : R² → R² given by 6x1+ 8x2 -7x1+ x2. T М —

A: We have to find the matrix of linear transformation.

Q: Determine whether the function involving the n x n matrix A is a linear transformation. :Mn.n Mn.n:…

Q: Suppose that T is a linear transformation such that - 9 - 3 Write T as a matrix transformation. For…

Q: Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0, 1) → (4, –1). (a) What is…

A: Follow step 2.

Q: Let T be the linear transformation defined by T(r1, x2, x3, x4) = -6x1 – 8x2+ x4. Find its…

Q: Consider the linear transformation T : R? → R defined by Т(х, у) —D (4х + 3у, —х + бу, —5х + 9у) If…

A: The given linear transformation T:ℝ2→ℝ3 defined by Tx,y=4x+3y, -x+6y, -5x+9y. If A is the standard…

Q: Suppose T:R –→ R² is a linear transformation with T(x1, x2, x3) Find the (standard) matrix A such…

A: The detailed solution is as follows below:

Q: Suppose T: M22→P3 is a linear transformation whos 11 1 0 = -2x3 -3x2-x+2 T = x2 0 1 0 0 Describe the…

Q: (d) Explain why every linear transformation T: R" → R™ is a matrix transformation.

A: Explanation: Let T:Rn→Rm is a linear transformation. Prove that the linear transformation T is a…

Q: Find a matrix A that induces the transformation T:R²→R³ given below. 6x-9y T| x+10y -3x+8y] [y

Q: Find a matrix A that induces the transformation T:R3R given below. |-8x-2y-2z -5x+6y+6z T

Q: The given formula defines a linear transformation. Give its standard matrix representation.…

Q: A ||

A: T:P2→P2 defined by Tft=f9t+6

Q: Suppose that T is a linear transformation such that (E)- (E) T = [-3], T = [-3], T = [5]. Write T as…

Q: 6. Let T be a linear transformation from R to R?given by T(x, x2x3) = (3x1 - 5x2 + X3, X1 + 6X3)…

Q: Find the standard matrix for the linear transformation T (æ, y) = (2x – 3y, x – y, y – 4æ) 3y, æ –…

Q: Determine whether the function involving the n × n matrix A is a linear transformation. T: Mn,n -…

A: Suppose T:Mn,n→Mn,n such that TA=4AX-4XA, where X is a fixed nxn matrix.To check: whether T is a…

Q: Find the standard matrix for the linear transformation T.T(x1, x2, x3, x4) = (0, 0, 0, 0)

A: Let Now,

Q: Show that the given transformation from R2 to R2 is linear by showing that it is a matrix…

A: Given: F reflects a vector in the y-axis

Q: Not every linear transformation T : R" → R™ is a matrix transformation.

Q: Let T be the linear transformation defined by T(x1, x2, x3, x4) : = x1 + 6x2 – 7x4. Find its…

Q: Find a matrix A that induces the transformation T:R2R³ given below. 4x+6y -8x-9y x-7y %3D

A: Here we use standard basis for R^2 and R^3. And then make a matrix by writing the elements in…

Q: (b) T(x1, x2, X3, X4) = (7x1 + 2x2 – x3 + x4, X2 + x3, -x1)

A: The given transformation in vector form is Tx1x2x3x4=7xx+2x2-x3+x4x2+x3-x1

Q: Let T be the linear transformation defined by T(х, у) %3D (-9у, 4х + у, 5у— 8х, 2у - 7x). Find its…

Q: Let 9 2 A 0 7 and B = Find the matrix C of the linear transformation T(x) = B(A(x)). C =

A: To find out the linear transformation given.

Q: Suppose A is a 5 x 7 matrix such that the linear transformation defined by T(x) = Ax is onto.…

Q: Consider the linear transformation T: R" HR", and its associated matrix A = [T(ëi) T(ë») T(em)] E…

A: Given linear transformation T: Rm -> Rn

Q: Construct the matrix for the transformation T:R → R whose input is an R vector given in its standard…

Q: Given: The linear transformation T: R² → R² first reflects points in the line x₂ = x₁ and then…

A: The standard basis of the vector space ℝ2 is 1,0, 0,1. In the first phase the points are reflected…

Q: Given the linear transformation: T:R3 - R* 4 0 2 2 4 4 -2 4 2 6 4 6 Find the image of the matrix…

Q: Suppose that T : R² → R´ is a linear transformation obeying 4 (). 7 and 13 Find the standard matrix…

Question

Define a linear transformation T : R² → R³ by
T(x1, x2) = (3x1 + x2, 5x1 + 7x2, 2x1 + 3x2)
Find a matrix representation for T. If you are not sure about your answer, at least state the size of
the matrix.

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

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Transformation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.