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The vectors u : = (2,-3,1), u2 = (1,4,-2), u3 = (-8,12,-4), uA = (1,37, 17), and u*, =

Chapter 1, Problem 7

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QUESTION:

The vectors u : = (2,-3,1), u2 = (1,4,-2), u3 = (-8,12,-4), uA = (1,37, 17), and u*, = (3, 5,8) generate R3 . Find a subset of the set {ui,u2,U3,U4,ur,} that is a basis for R

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QUESTION:

The vectors u : = (2,-3,1), u2 = (1,4,-2), u3 = (-8,12,-4), uA = (1,37, 17), and u*, = (3, 5,8) generate R3 . Find a subset of the set {ui,u2,U3,U4,ur,} that is a basis for R

ANSWER:

Step 1 of 5

Given that,

 

The basis for  consists of three independent vectors.

First, Check the linear independence and linear dependence of the vectors  .

After putting values of , we get that the vectors are linearly independent.

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