Suppose T is a linear transformation, whereT(ü)T(i)(1,0, 0)(- 3, 2)(0, 1, 0)(0,0, 1)(5, 4)T(w)(- 3, – 1)%3DFind the following:T(7ü + 35 + 8w) =(Enter vectors (x, y) using < x, y >)T((5,1,4)) =(Enter vectors (x, y) using < x, y >)

Answered: Image /qna-images/answer/87b3c264-4958-4508-9163-29875eb1859c.jpg

Suppose T is a linear transformation, where (1, 0, 0) T(ü) (- 3, 2) (0, 1, 0) T(7) (5, 4) (0,0, 1) T(ü) (- 3, – 1) Find the following: T(7u + 30 + 8w) = (Enter vectors (x, y) using < x, y >) %3D T((5,1, 4)) = (Enter vectors (r, y) using < x, y >)

Suppose T is a linear transformation, where (1, 0, 0) T(ü) (- 3, 2) (0, 1, 0) T(7) (5, 4) (0,0, 1) T(ü) (- 3, – 1) Find the following: T(7u + 30 + 8w) = (Enter vectors (x, y) using < x, y >) %3D T((5,1, 4)) = (Enter vectors (r, y) using < x, y >)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Q2. Let T: R³ R³ be a transformation defined by - ()-() T (a) Is T a linear transformation? Justify…

Q: Suppose T: R³ → R2 is a linear transformation with T(x1, x2, 3) = (-10x2, -5x1+11x2 - 7x3). Find the…

Q: (1' '3' Consider vị = | 2 V2 = 9 and v3 = 3 ) as vectors in R3. 4 Let T: R3→R2 be a linear…

Q: Show that the transformation T defined by T(x₁, x₂) = (2x₁ - 4x₂, x₁ +5, 6x₂) is not linear. If T is…

Q: Let e₁= (1,0), e₂ = (0, 1), ₁ = (1, -1) and ₂ = (-7,-3). Let T: R² → R² be a linear transformation…

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

A: Given that:T:ℝ3→ℝ3T1, 0, 0=2, -1, 4T0, 1, 0=-2, 3, 1T0, 0, 1=2, 0, -2To find: T-4, 2, 1

Q: Show that the transformation T defined by T(X₁, X₂) = (4x₁ - 2x₂₁ X₁ +3, 5x₂) is not linear. If T is…

Q: V₁ = (1,0), and let T: R² → R4 be the linear transformation T(v₁) = (6,0,3,1), Compute T(-3,2). V₂ =…

A: we need to compute T(-3, 2).

Q: Let L: R³ P2 be the linear transformation (no need to verify) defined by 3b 3c Let B₁ = b (2a-1/2-)…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Let T: R³ R³ be the linear transformation that does the following things, in this order, to an input…

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

Q: Suppose that T is a linear transformation from R2 to the space of 2 × 2 matrices which satisfies:…

Q: 2. Let T: R³ R² be a linear transformation such that Find T(1,2,1)= (1,0) T(2,9,0)= (-1,1) T(3,3,4)=…

Q: Suppose T: R2 → R2 is a linear transformation. The figure shows where I maps vectors V₁ and V2 from…

Q: Suppose T: R³-R² is a linear transformation. Three vectors U₁, U₂ and U3 are given below together…

Q: M = Find the matrix M of the linear transformation T: R³ → R² given by X1 3x1 = T (1:)) - [³ x2 X3 -…

A: We have to find the matrix .

Q: Find (a) the image of and (b) the preimage of for the linear transformation. T: R³ → R³, T(v, V2,…

Q: Ex.2. Let t : R3 → R3 be a linear transformation such that, t (а, b, c) %3 (За + с, — 2а + b, -а +…

Q: ppose that T : R² → R² is a linear transformation and that 7([일) -B] T and ar (H) nd T

Q: Let a = (d1, d2, a3, d4) where Let T: R4 → R4 be a linear transformation given by T(ते) = 31, T(dे०)…

Q: Let T:R" → R™ be a linear transformation and u, v E R", c is a scalar. Which of the following must…

Q: Suppose T is a linear transformation, where (1,0, 0) T(u) (4, – 5) %3D %3D (0, 1, 0) (- 3, – 5) (-…

Q: Suppose T: R³-R² is a linear transformation. Let U and V be the vectors given below, and suppose…

Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V→ R³ be a linear transformation for…

A: Given :T(v1)=(1,-1,2)T(v2)=(0,3,2)T(v3)=(-3,1,2)

Q: 3. Each of J, K, L, M and N is a linear transformation from R' to R?. These functions are given as…

Question

Suppose T is a linear transformation, where
T(ü)
T(i)
(1,0, 0)
(- 3, 2)
(0, 1, 0)
(0,0, 1)
(5, 4)
T(w)
(- 3, – 1)
%3D
Find the following:
T(7ü + 35 + 8w) =
(Enter vectors (x, y) using < x, y >)
T((5,1,4)) =
(Enter vectors (x, y) using < x, y >)

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

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, algebra and related others by exploring similar questions and additional content below.

Similar questions

4. Let B = {v1, v2, V3} and C = {w1, w2, w3} be bases for R3, with vectors defined below. -(:) -() --() v1 = V2 = V3 = and --(:) --E) --() 1 wi = , w2 = 1 , W3 = 1 Let L: R³ → R³ be the linear transformation defined by L: Find [L]B and [L]c, the matrices associated to L with respect to B and with respect to C.
Determine the matrix of the linear transformation T(x, y) = (3x + 5y, 3y – 2x) 5 -2 3 (a) -2 3 (b) (c) 3 3 3 (d) 3 3 -2 a 2]
Suppose T: R2-→R³ is a linear transformation. Let U and V be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(-3U-2V). 14 18 U = V = T(U) = -7 T(V) =-9 3 16 21 T(-3U–2V) = | 0
Let T: R R' be a linear transformation such that T(1, 0, 0) - (2, -1, 4), T(0, 1, 0) = (1, -2, 3), and T(0, 0, 1) = (-2, 0, 2). Find the indicated image. T(1, -4, 2) T(1, -4, 2) - (-10,18, – 6)
7. Let T : R² → R³ be a linear transformation with T(x1, x2) = (2x1 X2, -3x1 + - x2, 2x1 – 3x2). Can you find X (x1, x2) such that T(x1, x2) = (1,2, 3)?
(a) Let u and v be (fixed, but unknown) vectors in R". Suppose that T: R" → R" is a linear transformation such that T(u) = 6u + v and T(v) = 4u - 2v. Compute (T. T)(v), where TT is the composition of T with itself. Express your answer as a linear combination of u and v. (ToT)(v) = 10 u + -1 V Incorrect answer. Incorrect answer. (b) Let v and w be (fixed, but unknown) vectors in R", which are not scalar multiples of each others. Suppose that T: R" → R" is a linear transformation such that T(4v+3w) = -2v-2w and T(v+1w) = 5v+2w. Compute T(v) and express it as a linear combination of v and w. T(v) = 4 v + 2 W Incorrect answer. Incorrect answer.
Find the matrix of the linear transformation T from R2 - R² where T([1, 0]) = [1, –2] and T([2, 1]) = [2, 3] %3D (Note: matrix A = [T([1, 0]), T([0, 1])] 1 -2 (a) 1 (b) 1 (c) -2 (d) -2 3 7 3 Ob a C
Let f: R R be defined by f((x, y)) = 7y - 3x - 3. Is f a linear transformation? a. f((x₁, y₁) + (x₂, y₂)) = etc.) f((x₁, y₁>) + f((x₂, y₂)) = + Does f((x1, y₁) + (x2, Y2 )) = f ((x₁, y₁ )) + f((x2, Y₂ )) for all (x₁, y₁), (x2, Y₂) E R ²? choose b. f (c(x, y)) = c(f((x, y))) = Does f(c(x, y)) = c(f ((x, y))) for all c ER and all (x, y) ER ²? choose c. Is f a linear transformation? choose . (Enter x₁ as x1, <
Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are real numbers and, interpreting T as a matrix, det(T) # 0. Let P be the parallelogram which is the image of the square D = = [0, 1] × [0, 1] (i.e. T(D) =P). Then the area of P is given by O lad - bcl ad bc abcd 1 |ad - bc| O labcd|
Consider the linear transformation T:P (R) →P (R) defined by T (p(x)) = xp'(x). Which of the following statements is true about the vector y = x²+2x? O v is not the the range or nullspace. Ov is in the range but not the nullspace. Ov is in the nullspace but not the range. Ov is in both the nullspace and range.
Suppose T: R³-R² is a linear transformation. Let U, V and W be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(W). -3 3 2 3 ਪ = -3 -1 0 T(W) = 0 0 V = -3 W = | 3 - 1 T(I) = 0 T(V) = 0 -3
Suppose T: R³→R² is a linear transformation. Let U and V be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(−U+2V). 2 U = 1 3 4 V = 3 4 0 T(-U+2V) = 0 0 -6 [:] 6 T(U)= -9 [3] 9 T(V) =