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)
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:
Now we will solve the following system
b) To prove that the first vector can be expressed as a linear combination of the ...
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