Linear Algebra Please do not use any vector with JUST 1 and 0 numbers. Can use the online calculator to make it easier Try to show the steps.I have attached the image with the question. **Week 13: Part 1**Pick any three vectors \( u, v, w \) in \(\mathbb{R}^4\) which are linearly independent but not orthogonal, and a vector \( b \) which is not in the span of \( u, v, w \). If any of your vectors \( u, v, w \) are scalars of the standard basis vectors \( e_1, e_2, e_3, e_4 \) then start over. Let \( W = \text{span}\{u, v, w\} \).Compute the orthogonal projection \( \hat{b} \) of \( b \) onto the subspace \( W \) in two ways:1. Using the basis \(\{u, v, w\}\) for \( W \).2. Using an orthogonal basis \(\{u', v', w'\}\) obtained from \(\{u, v, w\}\) via the Gram-Schmidt process.Finally, explain in a few words why the two answers differ, and explain why only ONE answer is correct.

Answered: Image /qna-images/answer/34a30502-69de-4fd4-8350-ae7507af119d.jpg

Answered: Week 13: Part 1: Pick any three vectors…

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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Linear Algebra

Please do not use any vector with JUST 1 and 0 numbers.

Can use the online calculator to make it easier

Try to show the steps.

I have attached the image with the question.

**Week 13: Part 1**

Pick any three vectors \( u, v, w \) in \(\mathbb{R}^4\) which are linearly independent but not orthogonal, and a vector \( b \) which is not in the span of \( u, v, w \). If any of your vectors \( u, v, w \) are scalars of the standard basis vectors \( e_1, e_2, e_3, e_4 \) then start over. Let \( W = \text{span}\{u, v, w\} \).

Compute the orthogonal projection \( \hat{b} \) of \( b \) onto the subspace \( W \) in two ways:

1. Using the basis \(\{u, v, w\}\) for \( W \).
2. Using an orthogonal basis \(\{u', v', w'\}\) obtained from \(\{u, v, w\}\) via the Gram-Schmidt process.

Finally, explain in a few words why the two answers differ, and explain why only ONE answer is correct.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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