Question: Homework. 1. Use the vectors u = (u1, ..., Un), V = (v1, ..., Un), and w = (W1, ..., Wn) to verify the following

Homework.

1. Use the vectors u = (u1, ..., Un), V = (v1, ..., Un), and w = (W1, ..., Wn) to verify the following algebraic properties of R". ( a ) (utv) tw= u+ (v + w ) (b) c(utv) = cu + cv for each scalar c. 2. Let 0 6 10 A = OT b = co co and let W be the set of all linear combinations of the columns of A. (a) Is b in W? (b) Show that the third column of A is in W. 3. Let A be a 3 x 2 matrix. Explain why the equation Ax = b cannot be consistent for all b in R3. 4. Could a set of three vectors in R4 span all of R4? Explain. 5. Use technology to determine if the columns of the matrix span R4: 8 11 - 6 - 7 13 - 7 5 6 - 9 11 -6 4 1 8 Can a column be deleted so that the remaining columns still span R*? If so, find which column? Can you delete more than one? Why or why not

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