solution for ex : 2,4,6 PRACTICE PROBLEMS1. Prove that u + v =v + u for any u and v in R".2. For what value(s) of h will y be in Span{v. V2. V3) if-3VIV2 =V3 =and y =1.3 EXERCISESIn Exercises 1 and 2, compute u + v and u - 2v.1. u=2. u=2vIn Exercises 3 and 4, display the following vectors using arrowson an xy-graph: u, v. -v,-2v, u+ v, u- v, and u - 2v. Noticethat u - v is the vertex of a parallelogram whose other vertices areu, 0, and -v.-2v3. u and v as in Exercise I4. u and v as in Exercise 2In Exercises 5 and 6, write a system of equations that is equivalentto the given vector equation.7. Vectors a, b, c, and d8. Vectors w, x, y. and zIn Exercises 9 and 10, write a vector equation that is equivalent tothe given system of equations.5. x1-1+ x2X2 + 5x3 = 04.x + 6x2 - x3 = 09.10. 4x, + x2 + 3xrz = 96. x1+x2+ x3I - 7x - 2x3 = 2&x, + 6x2 - 5x3 = 15-x + 3x2 - 8x3 = 0Use the accompanying figure to write each vector listed in Exer-cises 7 and 8 as a linear combination of u and v. Is every vectorin R? a linear combination of u and v?In Exercises 11 and 12, determine if b is a linear combination ofa, az, and a;.

Answered: Image /qna-images/answer/9a7dc073-0cc0-469c-a367-f0e5db49ecd5.jpg

Answered: pute u + v and u - 2v. 目 …日 olay the…

pute u + v and u - 2v. 目 …日 olay the following vectors using arrows --2v, u + v, u- v, and u- 2v. Notice a parallelogram whose other vertices are

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 21EQ

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solution for ex : 2,4,6

PRACTICE PROBLEMS
1. Prove that u + v =v + u for any u and v in R".
2. For what value(s) of h will y be in Span{v. V2. V3) if
-3
VI
V2 =
V3 =
and y =
1.3 EXERCISES
In Exercises 1 and 2, compute u + v and u - 2v.
1. u=
2. u=
2v
In Exercises 3 and 4, display the following vectors using arrows
on an xy-graph: u, v. -v,-2v, u+ v, u- v, and u - 2v. Notice
that u - v is the vertex of a parallelogram whose other vertices are
u, 0, and -v.
-2v
3. u and v as in Exercise I
4. u and v as in Exercise 2
In Exercises 5 and 6, write a system of equations that is equivalent
to the given vector equation.
7. Vectors a, b, c, and d
8. Vectors w, x, y. and z
In Exercises 9 and 10, write a vector equation that is equivalent to
the given system of equations.
5. x1
-1
+ x2
X2 + 5x3 = 0
4.x + 6x2 - x3 = 0
9.
10. 4x, + x2 + 3xrz = 9
6. x1
+x2
+ x3
I - 7x - 2x3 = 2
&x, + 6x2 - 5x3 = 15
-x + 3x2 - 8x3 = 0
Use the accompanying figure to write each vector listed in Exer-
cises 7 and 8 as a linear combination of u and v. Is every vector
in R? a linear combination of u and v?
In Exercises 11 and 12, determine if b is a linear combination of
a, az, and a;.

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