In this question, you will apply the Gram-Schmidt process. The subspace V has a basis of three vectors u₁= 4₂= 0 and uz (c) Normalise v₂1, to give the vector v2. Enter the answer exactly. 14 -4 1 (a) Normalise vector ₁ to give the vector v1. Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example: [1/sqrt(2), 1/sqrt(3), 1/sqrt(6)]. (b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂.
In this question, you will apply the Gram-Schmidt process. The subspace V has a basis of three vectors u₁= 4₂= 0 and uz (c) Normalise v₂1, to give the vector v2. Enter the answer exactly. 14 -4 1 (a) Normalise vector ₁ to give the vector v1. Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example: [1/sqrt(2), 1/sqrt(3), 1/sqrt(6)]. (b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂.
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,...
Related questions
Question
please help solve all of these questions much appreciated
![In this question, you will apply the Gram-Schmidt process.
The subspace V has a basis of three vectors #₁ =
(c) Normalise v₂l, to give the vector v2. Enter the answer exactly.
(a) Normalise vector ₁ to give the vector v1.
Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example:
[1/sqrt(2), 1/sqrt(3), 1/sqrt(6)].
(f) Project the vector
(b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂!.
(g) Project the vector
42=
8
-16
6
(d) Find the component of u3 orthogonal to both v1 and v2. Enter the answer exactly. This will become the vector v3/.
5
3
(e) Normalise v3', to give the vector v3. Enter the answer exactly, possibly with a square-root. For example, the square root of 5 is entered as sqrt(5).
-3
and u3=
2
2
14
onto the same subspace.
-4
1
onto the subspace spanned by {1,2,3}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ac09755-9639-4075-b6f1-d2ae73f82d81%2F3511d82d-2661-4c03-8993-a9fea9953928%2Fo1r8w4l_processed.png&w=3840&q=75)
Transcribed Image Text:In this question, you will apply the Gram-Schmidt process.
The subspace V has a basis of three vectors #₁ =
(c) Normalise v₂l, to give the vector v2. Enter the answer exactly.
(a) Normalise vector ₁ to give the vector v1.
Note: You must enter your answer as a vector, using square brackets []. Enter each component in exact form, possibly with a square-root. For example:
[1/sqrt(2), 1/sqrt(3), 1/sqrt(6)].
(f) Project the vector
(b) Find the component of 2 orthogonal to ₁. Enter the answer exactly. This will become the vector v₂!.
(g) Project the vector
42=
8
-16
6
(d) Find the component of u3 orthogonal to both v1 and v2. Enter the answer exactly. This will become the vector v3/.
5
3
(e) Normalise v3', to give the vector v3. Enter the answer exactly, possibly with a square-root. For example, the square root of 5 is entered as sqrt(5).
-3
and u3=
2
2
14
onto the same subspace.
-4
1
onto the subspace spanned by {1,2,3}.
Expert Solution
Step 1: How to solve
As per our guidelines we are allowed to solve only three subparts of the given problem. Kindly repost the other subparts as separate one question.
I am going to solve the given problem by using some simple algebra to get the required result of the given problem.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education