Linear Algebra ### Problem 3Find each of the following for the vectors **u** = (1, -2, 3) and **v** = (0, 4, -1).#### (a) **u** · **v**Calculate the dot product of the vectors **u** and **v**.#### (b) ||**u** + **v**||Find the magnitude of the vector sum **u** + **v**.#### (c) A unit vector in the same direction as **v**.Determine the unit vector that has the same direction as **v**.

(a) u=1,-2,3, v=0,4,-1u.v=1,-2,3.0,4,-1 =1*0+-2*4+3*-1 =0-8-3 =-11 (b) u=1,-2,3,…

Answered: 3. Find each of the following for the…

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

### Problem 3

Find each of the following for the vectors **u** = (1, -2, 3) and **v** = (0, 4, -1).

#### (a) **u** · **v**

Calculate the dot product of the vectors **u** and **v**.

#### (b) ||**u** + **v**||

Find the magnitude of the vector sum **u** + **v**.

#### (c) A unit vector in the same direction as **v**.

Determine the unit vector that has the same direction as **v**.

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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