Consider M2,2, the vector space of real 2 x 2-matrices. For each of the following sets S, determine whether S is linearly independent or dependent. Linearly Dependent 1. S= Linearly Independent 2. S = Linearly Independent 3. S = 4 (16363 4 {[+] } -15 0 -10 1 -5 {[ ][ 1 Linearly Independent 4. S = { - " -15 -5 4 -15 -10 5 {]} -5 ].[ 0 [3][72]} [1/7 -5 -1 5

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 18E: Prove part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix...
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Note: there is no partial credit for this problem. You must answer all parts correctly to receive credit. You will not be
shown the correct answers for individual parts.
Consider M2,2, the vector space of real 2 x 2-matrices. For each of the following sets S, determine whether S is linearly
independent or dependent.
Linearly Dependent
1. S =
Linearly Independent 2. S =
Linearly Independent
3. S =
Linearly Independent 4. S=
3 4 4
4 4
{[³1] [63] [63])}
4
3
-15
0
{[ + ][ - ] }
-10
5
{[³
{[7]-[-25 $]}
17 -31
3
{ [²7²2]}
{[³
"
-15
-10
0
9].
-3
10
"
-
5
3
Transcribed Image Text:Note: there is no partial credit for this problem. You must answer all parts correctly to receive credit. You will not be shown the correct answers for individual parts. Consider M2,2, the vector space of real 2 x 2-matrices. For each of the following sets S, determine whether S is linearly independent or dependent. Linearly Dependent 1. S = Linearly Independent 2. S = Linearly Independent 3. S = Linearly Independent 4. S= 3 4 4 4 4 {[³1] [63] [63])} 4 3 -15 0 {[ + ][ - ] } -10 5 {[³ {[7]-[-25 $]} 17 -31 3 { [²7²2]} {[³ " -15 -10 0 9]. -3 10 " - 5 3
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