just answer the question 4, thanks 3. (9 points) For the following, be sure to j

Question

just answer the question 4, thanks

3. (9 points) For the following, be sure to justify your answer. (a) (3 points) How many pivot columns must a 5 × 4 matrix have if its columns are linearly independent? Justify your answer. Justify your answer Explain. (b) (3 points) How many pivot columns must a 4 x 6 matrix have if its columns span R'? (c) (3 points) Let A be a 4x 5 matrix. Can the columns of A be linearly independent? (9 points) No explanation necessary for these questions (a) Give an example of a set of vectors in R3 that are linearly dependent and span R3 (b) Give an example of a set of vectors in R3 that are linearly independent and do not span IR 3 (c) Give an example of a set of vectors in IR3 that are linearly independent and span R

Explanation / Answer

a.

{(1,0,0),(0,1,0),(0,0,1),(0,0,2)}

Linearly dependent as we see 4th vector is multiple of 3rd and first three are standard basis vectors of R3

b.

{(1,0,0),(0,1,0)}

c)

{(1,0,0),(0,1,0),(0,0,1)}

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