Let i (first three digits), v = (last four digits) %3! !! 2 15 7 49 Let A = l2 1 5 7 4 9 1 (place your whole ID in each row) Calculations. 1. Compute (u, b). Determine ||||. Write the answer as a simplified square root. 3. Calculate the angle between u and v in radians. Round answer to four decimal places. O211
Let i (first three digits), v = (last four digits) %3! !! 2 15 7 49 Let A = l2 1 5 7 4 9 1 (place your whole ID in each row) Calculations. 1. Compute (u, b). Determine ||||. Write the answer as a simplified square root. 3. Calculate the angle between u and v in radians. Round answer to four decimal places. O211
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
100%
![MAT280 Fall2020 TakeHome 119 update - Word
Riley Cyron
RC
Mailings
Review
View
Help
A Share
Home
Insert
Design
Layout
References
Let å =
(first two ID digits), =
(middle three ID digits), 2=| 1 (last two digits)
Let i =
(first three digits), v =
(last four digits)
1 5
7 4
9
Let A =
(place your whole ID in each row)
15 7 4 9 1
Calculations.
1. Compute (u, 3).
Determine ||v||. Write the answer as a simplified square root.
3. Calculate the angle between u and v in radians.
Round answer to four decimal places.
4. Construct projzv. Round each component to four decimal places.
5.
Let p = 2+3x - x3. Determine the coordinate matrix of p relative
to the basis B = {1,1 – x, 1 + x²,1 – x3}.
6. Construct the orthogonal complement S for S = span{u, v}.
7. Use the Gram-Schmidt Process to construct an orthonormal basis
for the vector space V = span{d, b, č}.
Round answers to four decimal places, where necessary.
8. Consider the basis B = {(2, -V2), (2, V2)} for R?. Define (3, z) =y,z1 +y22.
%3D
a) Verify that B is an orthonormal basis.
b) Calculate [w], for w = (20,-6V2).
9. Define a linear transformation T: R → R² by T(X) = Ax.
Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2).
b) Calculate the pre-image of (60, 120).
c) Determine a basis of the range of the transformation.
d) Determine a basis for the kernel of the transformation.
10. Define T: R3 → R such that T (à) = (1,2,1), T(b) = (0,1,3),T(C) = (1,0,–1).
Calculate T(-2,3,-1).
11. Define T: R? → R² by T(x, y) = (3x – 2y, y – 2x).
a) Construct the standard matrix for T.
b) Construct the matrix for T relative to the basis {(5,2), (2,1)}.
c) Construct the matrix for T1 relative to the basis {(1,1), (1,2)}.
in 74](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30964914-193b-4e8f-b933-192cb468e42e%2Fe6fb12fd-8fef-4500-a357-766a45b4eff4%2Fpo07dr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:MAT280 Fall2020 TakeHome 119 update - Word
Riley Cyron
RC
Mailings
Review
View
Help
A Share
Home
Insert
Design
Layout
References
Let å =
(first two ID digits), =
(middle three ID digits), 2=| 1 (last two digits)
Let i =
(first three digits), v =
(last four digits)
1 5
7 4
9
Let A =
(place your whole ID in each row)
15 7 4 9 1
Calculations.
1. Compute (u, 3).
Determine ||v||. Write the answer as a simplified square root.
3. Calculate the angle between u and v in radians.
Round answer to four decimal places.
4. Construct projzv. Round each component to four decimal places.
5.
Let p = 2+3x - x3. Determine the coordinate matrix of p relative
to the basis B = {1,1 – x, 1 + x²,1 – x3}.
6. Construct the orthogonal complement S for S = span{u, v}.
7. Use the Gram-Schmidt Process to construct an orthonormal basis
for the vector space V = span{d, b, č}.
Round answers to four decimal places, where necessary.
8. Consider the basis B = {(2, -V2), (2, V2)} for R?. Define (3, z) =y,z1 +y22.
%3D
a) Verify that B is an orthonormal basis.
b) Calculate [w], for w = (20,-6V2).
9. Define a linear transformation T: R → R² by T(X) = Ax.
Calculate the image of (1, 0, 2, 1, 2, -1, 1, 2).
b) Calculate the pre-image of (60, 120).
c) Determine a basis of the range of the transformation.
d) Determine a basis for the kernel of the transformation.
10. Define T: R3 → R such that T (à) = (1,2,1), T(b) = (0,1,3),T(C) = (1,0,–1).
Calculate T(-2,3,-1).
11. Define T: R? → R² by T(x, y) = (3x – 2y, y – 2x).
a) Construct the standard matrix for T.
b) Construct the matrix for T relative to the basis {(5,2), (2,1)}.
c) Construct the matrix for T1 relative to the basis {(1,1), (1,2)}.
in 74
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!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps
Knowledge Booster
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.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
