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Determine whether or not the vectors are linearly dependent. Determine whether or not the vectors u = (1, 1, 1)^T, v = (2, 3, 1)^T, w = (4, 5, 5)^T in R^3, are linearly dependent. Solution The vectors are dependent if 2 vector by some combination add up to 3rd vector. Lets see. if we add 2u + v we get (2+2,2+3,2+1) = (4,5,3) which is different than (4,5,5) Hence, its never possible to acheive a combination such that a vector is some sum of other 2 vectors. Hence, these are indepedent..

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Determine whether or not the vectors are linearly dependent. Determine whether or not the vectors u = (1, 1, 1)^T, v = (2, 3, 1)^T, w = (4, 5, 5)^T in R^3, are linearly dependent. Solution The vectors are dependent if 2 vector by some combination add up to 3rd vector. Lets see. if we add 2u + v we get (2+2,2+3,2+1) = (4,5,3) which is different than (4,5,5) Hence, its never possible to acheive a combination such that a vector is some sum of other 2 vectors. Hence, these are indepedent.

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  • 1. Determine whether or not the vectors are linearly dependent. Determine whether or not the vectors u = (1, 1, 1)^T, v = (2, 3, 1)^T, w = (4, 5, 5)^T in R^3, are linearly dependent. Solution The vectors are dependent if 2 vector by some combination add up to 3rd vector. Lets see. if we add 2u + v we get (2+2,2+3,2+1) = (4,5,3) which is different than (4,5,5) Hence, its never possible to acheive a combination such that a vector is some sum of other 2 vectors. Hence, these are indepedent.