Answered: 1. For the following subsets of R3,… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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1. For the following subsets of R3, explain whether or not they are a subspace of R³.
(a)
(b)
1.1
0.65
U
= span
-3.4
0.23
0.4
-0.44
0
(})}
a
V
{(2) | ER
(c) Z= the points in the z-axis

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Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Q6: Explain whether the following sets are not subspaces of R" for the appropriate value of n. a a a (a) U = a+b = d-e a2 -3 (b) V = + 2b – c= 2 (c) W = 2a = bte e-d = 0 |el < 4
Answer the following: JAIAI OT VOITOU0 4. Determine if the odd functions (f(-x) = -f(x)) are a subspace of C(-o,0)
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1. Determine whether the set W =- X1,X, E R,x, = 0}} is a subspace of R' with the standard operations. Justify your answer.
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2. Find the projection from R³ onto its subspace spanned by (1,2,−1)ª and (1,1,2).
5) For each of the following subsets of F’, determine whether it is a subspace of F3 : (where Fis either C, R,or Q a) x1 + 2x2 + 3x3 = 0} b) X2 x1 + 2x2 + 3x3 = c) X2 |x1x2x3 (X3. d) X2x1 = 5x3 %3D
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3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a subspace of R2? Justify your answer.
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