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Exercise 6. Consider the following vectors in R3 . v1 = (1, −1, 0) v2 =...

Exercise 6. Consider the following vectors in R3 . v1 = (1, −1, 0) v2 = (3, 2, −1) v3 = (3, 5, −2 )   (a) Verify that the general vector u = (x, y, z) can be written as a linear combination of v1, v2, and v3. (Hint : The coefficients will be expressed as functions of the entries x, y and z of u.) Note : This shows that Span{v1, v2, v3} = R3 . (b) Can R3 be spanned by two vectors w1 and w2 ? Be sure to justify your answer. (Hint : Rephrase this question in terms of the consistency of a suitable linear system ).

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