For each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two.(a) (-2,0,3) ,(1,3,0),(2,4,-1)(b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1)(c) (3,4,1) ,(1,-2,1), (-2,-1,1)(d) (2,-1,0) , (1,2,-3), (1,-3,2)(e) (5,1,-5) , (1,-2,-3), (-2,3,-4)(f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)

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Asked Dec 27, 2019
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For each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two.

(a) (-2,0,3) ,(1,3,0),(2,4,-1)

(b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1)

(c) (3,4,1) ,(1,-2,1), (-2,-1,1)

(d) (2,-1,0) , (1,2,-3), (1,-3,2)

(e) (5,1,-5) , (1,-2,-3), (-2,3,-4)

(f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)

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Expert Answer

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

To prove that the first vector can be expressed as a linear combination of the other two we have to find alpha and beta in R (Real number) such that:

Algebra homework question answer, step 1, image 1
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Step 2

Now we will solve the following system

 

Algebra homework question answer, step 2, image 1
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Step 3

b) To prove that the first vector can be expressed as a linear combination of the ...

Algebra homework question answer, step 3, image 1
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