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Asked Oct 15, 2019
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linear algebra

(5) Show that the following three vectors in R3 form a linearly independent set
-))-()
2
1
1
2
3
3
2
Can
be written as a linear combination of u2 and us?
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(5) Show that the following three vectors in R3 form a linearly independent set -))-() 2 1 1 2 3 3 2 Can be written as a linear combination of u2 and us?

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Expert Answer

Step 1

To prove the linear independence of the three given vectors.

Step 2

We prove that they are linearly independent by showing that there is no linear lin...

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Consider any relation 2 1 1 -1 b2 +c-3 a -3 2 then 2a+b+c = 0_(1) - a2b-3c = 0 (2) - 3b+2c = 0 (3) (1)(2)(3) a = 0, b= 0,c = 0 so bc 0,2b-3c = 0 This proves the linear independence.

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