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3. Suppose that T is a linear transformation with the matrix of the transformation: A = [1 Determine if T is one-to-one. Determine if T is onto. 2 1 Lo -2 5 3 -5 ܗ -2 -4 11 4 a. Suppose that T:R → Rm. What is n and what is m? b. Find Ker (T). C. Find Rng(T) d. e.

3. Suppose that T is a linear transformation with the matrix of the transformation: A = [1 Determine if T is one-to-one. Determine if T is onto. 2 1 Lo -2 5 3 -5 ܗ -2 -4 11 4 a. Suppose that T:R → Rm. What is n and what is m? b. Find Ker (T). C. Find Rng(T) d. e.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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SOlve #3, Show all of your steps and all of your work please. Post your work on pictures please!

3. Suppose that T is a linear transformation with the matrix of the transformation: A = C. d. Determine if T is one-to-one. e. Determine if T is onto. 1 a. b. c. 1 Lo a. Suppose that T:R" → Rm. What is n and what is m? b. Find Ker (T). Find Rng(T) -2 5 3 -4 -5 11 4 -2 4. Suppose that V = Cº[0, 1], and let (f(x), g(x)) = integrate. Show what you put into the calculator as well as the results. Find (x, 2x³). Find ||3x|| f(x) g(x) dx. You may use a calculator to Determine if f(x) = cos (x) and g(x) = sin(x) is orthogonal. Explain your reasoning. 5. Use projections to find the distance from the point (0, -1, 3) to the plane 2x-3y+z=4. Show your work. Write your answer as an exact answer and not as a decimal. You may use a calculator. 6. General Rank Nullity states: If T: VW is a linear transformation and V is finite-dimensional, then dim[Ker(T)]+dim[Rng(T)]=dim[V]. Use this information to answer the following questions: Suppose that the Kernel of T was a 2-dimensional subspace of R5 and W is R³. a. What is V? b. Is T onto, explain how you know? c. Is T one-to-one? Explain how you know.
Transcribed Image Text:3. Suppose that T is a linear transformation with the matrix of the transformation: A = C. d. Determine if T is one-to-one. e. Determine if T is onto. 1 a. b. c. 1 Lo a. Suppose that T:R" → Rm. What is n and what is m? b. Find Ker (T). Find Rng(T) -2 5 3 -4 -5 11 4 -2 4. Suppose that V = Cº[0, 1], and let (f(x), g(x)) = integrate. Show what you put into the calculator as well as the results. Find (x, 2x³). Find ||3x|| f(x) g(x) dx. You may use a calculator to Determine if f(x) = cos (x) and g(x) = sin(x) is orthogonal. Explain your reasoning. 5. Use projections to find the distance from the point (0, -1, 3) to the plane 2x-3y+z=4. Show your work. Write your answer as an exact answer and not as a decimal. You may use a calculator. 6. General Rank Nullity states: If T: VW is a linear transformation and V is finite-dimensional, then dim[Ker(T)]+dim[Rng(T)]=dim[V]. Use this information to answer the following questions: Suppose that the Kernel of T was a 2-dimensional subspace of R5 and W is R³. a. What is V? b. Is T onto, explain how you know? c. Is T one-to-one? Explain how you know.
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