10 Let a₁ = , a₂ = a35 , and b = Determine whether b can be written as a linear combination of a₁, a2, and a3. In other words, determine whether weights xX₁, X2, and x3 exist, such that x₁ a₁ + x2 a2 + x3 a3 = b. Determine the weights X₁, X2, and x3 if possible. Ox₁=-3, x₂ = 0, x3 = 1 No solution OX₁-2, X₂=-1, X3 = -6 0x₁=2₁x₂=1, X3-0 A

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
icon
Related questions
Question
8.0
Let a₁ =
,a₂
a3 =
, and b =
Determine whether b can be written as a linear combination of a₁, a2, and a3. In other words, determine whether weights X₁, X2,
and x3 exist, such that x₁ a₁ + x2 a2 + x3 a3 = b. Determine the weights x₁, x2, and x3 if possible.
Ox₁=-3, X2=0, x3 = 1
No solution
OX₁-2, X₂=-1₁ X3 = -6
0x₁=2, X₂=1x3-0
Previous
Next ▸
Quiz saved at 11:14pm
Submit Quiz
Transcribed Image Text:8.0 Let a₁ = ,a₂ a3 = , and b = Determine whether b can be written as a linear combination of a₁, a2, and a3. In other words, determine whether weights X₁, X2, and x3 exist, such that x₁ a₁ + x2 a2 + x3 a3 = b. Determine the weights x₁, x2, and x3 if possible. Ox₁=-3, X2=0, x3 = 1 No solution OX₁-2, X₂=-1₁ X3 = -6 0x₁=2, X₂=1x3-0 Previous Next ▸ Quiz saved at 11:14pm Submit Quiz
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning