(4) Consider two nonzero vectors 21 Y1 22 Y2 x = R, and y Rn I'm Yn What is the rank of the matrix

(cf) Consider two nonzero vectors m1 \"HI 1'2 L's a: = : E aim: and y = : E at\": Im n What is the rank of the matrix A = my'? Explain your reasoning. In feet, the converse of your conclusion here also holds: an}; matrix A that has the rank of your answer in {b} can he expressed as A 2 ref for some nonzero vectors a: and 1; {you can think about why; this is not required to he part your answer for part [13)]

(4) Consider two nonzero vectors 21 Y1 22 Y2 x = R", and y Rn I'm Yn What is the rank of the matrix A = xy'? Explain your reasoning. In fact, the converse of your conclusion here also holds: any matrix A that has the rank of your answer in (b) can be expressed as A = xy' for some nonzero vectors x and y (you can think about why; this is not required to be part your answer for part (b)).