Given the d. subspace V={(x,y,z)=R³ | 2x+y-z=0} of the d. space (R³(R),+,-) and the vector =(3,-5,1)=R³. ind a basis B₁ of V and then prove that the set B2 ={(-1,3,1),(-1,4,2)} is also a basis of V, 1#B2. Give the coordinates of the vector u to the base B₁

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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EX 8A
Given the d. subspace V={(x,y,z)=R³ | 2x+y-z=0} of the d. space (R³(R),+,·) and the vector
u=(3,-5,1)=R³.
Find a basis B₁ of V and then prove that the set B2 ={(-1,3,1),(-1,4,2)} is also a basis of V,
B1 B2. Give the coordinates of the vector u to the base B₁
Transcribed Image Text:EX 8A Given the d. subspace V={(x,y,z)=R³ | 2x+y-z=0} of the d. space (R³(R),+,·) and the vector u=(3,-5,1)=R³. Find a basis B₁ of V and then prove that the set B2 ={(-1,3,1),(-1,4,2)} is also a basis of V, B1 B2. Give the coordinates of the vector u to the base B₁
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