4. Find a base and the Range for the space generated by: V₁= (1.-2,0,0,3) V₂=(2,-5,-3,-2,6) V3= (0,5,15,10,0) V4 (2,6,18,8,6)

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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4. Find a base and the Range for the space generated by:
V₁= (1,-2,0,0,3) V₂=(2,-5,-3,-2,6) V3 (0.5,15,10,0) V4 (2,6,18,86)
Transcribed Image Text:段階的に解決し、 人工知能を使用せず、 優れた仕事を行います ご支援ありがとうございました SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI DON'T USE AI DON'T USE AI DON'T USE AI 4. Find a base and the Range for the space generated by: V₁= (1,-2,0,0,3) V₂=(2,-5,-3,-2,6) V3 (0.5,15,10,0) V4 (2,6,18,86)
Expert Solution
Step 1: vectors

vectors are V 1 space equals space open square brackets table row 1 row cell negative 2 end cell row 0 row 0 row 3 end table close square brackets comma space V 2 space equals space open square brackets table row 2 row cell negative 5 end cell row cell negative 3 end cell row cell negative 2 end cell row 6 end table close square brackets space comma space V 3 space equals space open square brackets table row 0 row 5 row 15 row 10 row 0 end table close square brackets space comma space V 4 space equals space open square brackets table row 2 row 6 row 18 row 8 row 6 end table close square brackets


the row reduced echelon form 

open square brackets table row 1 0 0 cell negative 2 end cell 3 row 0 1 0 cell negative 1 end cell 0 row 0 0 1 1 0 row 0 0 0 0 0 end table close square brackets

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