Question

Write each vector as a linear combination of the vectors in S. (Use s1 and s2,...

Write each vector as a linear combination of the vectors in S. (Use s1 and s2, respectively, for the vectors in the set. If not possible, enter IMPOSSIBLE.)

S = {(1, 2, −2), (2, −1, 1)}

(a)    z = (−5, −5, 5)
z = ?

(b)    v = (−2, −6, 6)
v = ?


(c)    w = (−1, −17, 17)
w = ?

Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, s2, and s3, respectively, for the vectors in the set.) S = {(1, 2, 3, 4), (1, 0, 1, 2), (1, 4, 5, 6)}

(0, 0, 0, 0) = ?


Express the vector s3 in the set as a linear combination of the vectors s1 and s2.

s3 = ?

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