Let (x, y, z) E R³ and the transformation T: R³ → R² be given byT(x, y, z) = (2.x + 4y, x + 3y + 2).Find the standard matrix for T and decide whether the transformation Tis invertible. If yes, then find the inverse transformation, and if not, thenexplain why.

Transformation is invertible if and only if transformation is square.

Answered: Let (x, y, z) E R and the…

Math

Advanced Math

Let (x, y, z) E R and the transformation T: R³ → R² be given by T(x, y, 2) = (2.x + 4y, x + 3y + 2).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 12CM

See similar textbooks

Related questions

Q: Show that the mapping T: R → R defined by T (x, y, z) = (| x, 0) is not a linear transformation.

Q: Let L : P1 → P1 be a linear transformation defined by L(t − 1) = t + 2 and L(t + 1) = 2t + 1. (a)…

A: Given, L : P1 → P1 be a linear transformation defined byL(t − 1) = t + 2 and L(t + 1) = 2t + 1

Q: One of the following is not a linear transformation (a) T : R² → R³ defined by T(x, y) = (x, xy, x)…

Q: Let ƒ : R → R be defined by f(x) = 1 – 5x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) +…

A: Substitute x+y for x in the equation fx=1-5x and simplify to calculate the value of fx+y.…

Q: Let f : R? → R be defined by f((x, y)) = 5x + 7y. Is ƒ a linear transformation? c. Is f a linear…

Q: (b) Prove that the mapping T:R2 → R³ from R² into R³, defined by T(x, y) = (x + 1,2y, x + y) is not…

A: A mapping T is a linear transformation if and only if a) T(x+y) = T(x)+T(y) b) T(ax) = aT(x)

Q: Let f: RR be defined by f(x) = -8x?. Is f a linear transformation? a. f(x +y) =|-8x2-8y2-16xy f(x) +…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: One of the following is not a linear transformation (a) T: R R' defined by T(r. y) = (x, xy. T) (b)…

A: In the question one of the following transformation is not a linear transformation. First we will…

Q: T is a linear transformation from R² into R². Show that T is invertible and find a formula for

Q: 25) Show that the linear transformation T(x, y, z) = (x - 2y, -x+y+z, x+y) is n isomorphism, and…

Q: Find the kernel of the linear transformation.T: R2→R2, T(x, y) = (x + 2y, y − x)

A: Given, the linear transformation is T: R2 to R2 s.t. T(x, y) = (x+2y,…

Q: Give a counterexample to show that the given transformation is not a linear transformation.

A: To show this T xy=|x||y| is not linear transformation by counter example.

Q: Let T(x, y) = (-x – y, 3x – 3y). Let D* be [, 1] × [0, 1] and D be the image of D* under the…

Q: #2. Given the linear transformation T : R2→R?defined by T(x, y) = (10x + 3y, 6x + 2y), find the…

Q: Question 3. a) Consider the map T : R² → R³ defined by T(x, y) = (x,0, y). Is T a linear…

A: The solution is given as

Q: Let f : R → R° be defined by f(x) = (-2x, 7x, 7x). Is ƒ a linear transformation? a f(r + y) f(r)+…

Q: If T : V → W and U : W → Z are linear transformations, prove that rank(UT) < rank(T). (Hint: How…

Q: 4. Let T: RR be defined by T(r, y, 2) = (4x - 3y + 4z, a+ 2y - z, 5r – y+ 3z) Show that T is a…

A: Explanation of the answer is as follows

Q: 5. Prove that the transformation T: R²R defined by T(x, y) = 5y-k is linear only if k = 0.

A: The given transformation is T:R2→R defined by Tx,y=5y-k

Q: Let T: R³ R³, T(x, y, z) = (8x + 7z, y, 9x + 8z) be an invertible linear transformation. The inverse…

Q: Let f : R → R° be defined by f(x) = (x, -3x?, 5x). Is fa linear transformation? a. f(x + y) = f(x)+…

Q: Consider the transformation T of R to R2 defined by T(x,y,z)= (3x, 2y+z). The image of (1,2,3) is: O…

Q: give a counterexample to show that the given transformation is not a linear transformation.

A: Given, A linear transformation,

Q: (a) Assume T R2 R is a linear transformation with T(1,0) = 3 and T(0, 1) = -1. Calculate T(2,5). (b)…

Q: If T: R3 → R is a linear transformation such that T (E) then T

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: Calculate the nullity n(T) for the linear transformation T defined by T(r, y, z) = (r+ 2y + 2, -r+…

A: Given : a linear transformation T defined by Tx, y, z=x+2y+z, -x+3y+z To find : nullity nT

Q: Show that the function T : Pn → R defined by T(r0+r1x+· · ·+rnx^n) = rn is a linear transformation.

A: Given that, the functionT:Pn→R defined byT(r0+r1x+···+rnxn)=rn

Q: Let F: R3 → R4 be a linear transformation. f (x, y, z) = (x, x + 3y, x, x + z) Is f bijective?

A: A function f is said to be bijective if and only if it is both injective(one to one) and surjective…

Q: Map the image of Ay=x^(1/2) on the w- plane of transformation w=B *Z^2 Assume all missing or error…

A: Given: Now the given are, On the w-plane of the transformation w=B *Z2, map the image of…

Q: Let u = u(x, y) By using the transformation r = -2x + y2 find uxy = s = 2x + y?,

A: Let u=u(x,y) And transformations r=-2x+y2 s = 2x+y2 To determine uxy uxy=urrrxry +…

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: 9. Show that the function T: R³ → R3 defined by T(r, y, z) = (x – z, 2x + y, 2y – 3x) %3D is a…

Q: Let f : R → R be defined by f((x, y)) = 9x + 6y. Is ƒ a linear transformation? a. f((r1, Y1) + (x2,…

Q: T is a transformation defined by T(P) = (Vx – 5,y – 8) for all points P(x,y) E u. Find out if T is…

Q: 7. Show that the transformation T: R →R defined by T (x, y, z) = (x– y, 0, y + z) is a linear…

Q: Let f: R R° be defined by f(x)= (-4x,7x,-3x 6). Is fa linear transformation? a. f(x + y) = f(x) +…

A: f: ℝ3→ℝ3 be defined by fx=-4x, 7x, -3x-6 (a) fx+y=-4x+y, 7x+y, -3x+y-6⇒fx+y=-4x-4y, 7x+7y,…

Q: Consider at linear transformation T(#) = A¤, where A E R"x8, such that dim(ker(A))= 3. What is dim(…

A: We will find out the required value.

Q: Calculate the nullity 7(T) for the linear transformation T defined by T(x, y, z) = (x +2y + z, -1 +…

A: Determine the span of the function. Now use it to determine the dimension of N(T). Now use the…

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

Q: (;)-(; x – 3y -2x + 3y 5у — 4 Consider the transformation T : R² → R³ given by T %3D (a) Verify that…

A: Solution :-

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: Suppose T:R2 → R² is defined by T(x,y) = (x - y, x+2y) then T is .a Linear transformation .b…

A: The solution is given as

Q: Let f : R → R be defined by f(x) = -9x². Is f a linear transformation? a. f(x + y) = f(x) + f(y) = +…

Q: 1)if T : R? R? (x, y) Т(1, у) :3 (ал + by, сz + dy) %3D is a linear transformation such that T (2,…

Q: 1. Find the image of the line that passes through the point (1, 1) and is parallel to the = under…

Q: If a transformation T: R" → Rm satisfies T(0) = 0, then it is a linear transformation. True False

Q: Given that the linear transformation T: Pg R has nullity 3. Then the rank of T is equal to:

Q: Suppose T is the transformation from R2 to R2 that results from a reflection over the x-axis…

Question

Let (x, y, z) E R³ and the transformation T: R³ → R² be given by
T(x, y, z) = (2.x + 4y, x + 3y + 2).
Find the standard matrix for T and decide whether the transformation T
is invertible. If yes, then find the inverse transformation, and if not, then
explain why.

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

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.