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Consider the following vectors: -3 6 = | b2 || b3 where b1, b2 and b3 are any real numbers. Show that there exists a linear combination of ū, i and w that is equal to b, i.e., there exist scalars c1, C2 and c3 such that cữ + c20+ c3w = b. Hint: Write down the corresponding system of equations and use back substitution.

Consider the following vectors: -3 6 = | b2 || b3 where b1, b2 and b3 are any real numbers. Show that there exists a linear combination of ū, i and w that is equal to b, i.e., there exist scalars c1, C2 and c3 such that cữ + c20+ c3w = b. Hint: Write down the corresponding system of equations and use back substitution.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 29E
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Consider the following vectors: 4 b1 U = 1 b2 b3 where b1, b2 and b3 are any real numbers. Show that there exists a linear combination of ū, i and w that is equal to b, i.e., there exist scalars C1, C2 and c3 such that cu + C2v + C3w = b. Hint: Write down the corresponding system of equations and use back substitution.
Transcribed Image Text:Consider the following vectors: 4 b1 U = 1 b2 b3 where b1, b2 and b3 are any real numbers. Show that there exists a linear combination of ū, i and w that is equal to b, i.e., there exist scalars C1, C2 and c3 such that cu + C2v + C3w = b. Hint: Write down the corresponding system of equations and use back substitution.
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