# A what is n n 3 this is the size of each u i b what

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Chapter 10 / Exercise 1
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
(a) What is n ? (b) What is m ?
(c) Are u , . . . , u linearly independent?
1 m (d) Does { u , . . . , u } span R n ?
1 m (e) Looking at B can you write down a subset of the original set { u , . . . , u } that
1 m would be guaranteed to be linearly independent? (f) Is there a subset of the original set { u , . . . , u } that would be guaranteed to
1 m span R n ?
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Chapter 10 / Exercise 1
Mathematical Applications for the Management, Life, and Social Sciences
Harshbarger
Expert Verified
(g) Write down a b R n for which Bx = b does not have a solution. (h) Write down a b R n for which Bx = b has a solution. (i) Write down a b R n for which Bx = b has a unique solution. (j) Is there a new vector w R n that you could add to the set { u 1 , . . . , u m } to guarantee that { u 1 , . . . , u m , w } will span R n ? (k) Is there a column of B that is in the span of the rest? If so, find it. (l) Looking at B do you see a u i that is in the span of the others? How can you identify it? (m) Assuming that no row of A was a zero row, how many planes are being used to cut out the solutions of Ax = 0?