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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
SOlve #5, Show all of your steps and all of your work please. Post your work on pictures please! show a graph and the formula you are using
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0655393b-8df3-4633-b13c-e0d6983d2306%2F197a6b6f-4012-4ff9-88f8-cb25dc81212f%2F777cyo_processed.png&w=3840&q=75)
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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