Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 0 0-1 4 1 1 -8 2 1 - 16 O

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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Question
Determine if the columns of the matrix form a linearly independent set.
Justify your answer.
-2 -1
0
- 1
1
1
2
1
0
4
- 8
- 16
Transcribed Image Text:Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 0 - 1 1 1 2 1 0 4 - 8 - 16
Expert Solution
Step 1: We use row reduction of this matrix.

open square brackets table row cell negative 2 end cell cell negative 1 end cell 0 row 0 cell negative 1 end cell 4 row 1 1 cell negative 8 end cell row 2 1 cell negative 16 end cell end table close square brackets

R subscript 3 rightwards arrow 2 R subscript 3 plus R subscript 1 comma space space space R subscript 4 rightwards arrow R subscript 4 plus R subscript 1
open square brackets table row cell negative 2 end cell cell negative 1 end cell 0 row 0 cell negative 1 end cell 4 row 0 1 cell negative 16 end cell row 0 0 cell negative 16 end cell end table close square brackets

R subscript 3 rightwards arrow R subscript 3 plus R subscript 2 comma
open square brackets table row cell negative 2 end cell cell negative 1 end cell 0 row 0 cell negative 1 end cell 4 row 0 0 cell negative 12 end cell row 0 0 cell negative 16 end cell end table close square brackets

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