Conversely, suppose y belongs to Col Q. Then y = Qx for some x. Since R is invertible, what does the equation A = QR imply? A. Q= AR 1 O B. A=Q. OC. Ais invertible. O D. Q=R 'A So y = , which shows...

Extracted text: Conversely, suppose y belongs to Col Q. Then y = Qx for some x. Since R is invertible, what does the equation A = QR imply? A. Q= AR 1 O B. A=Q. OC. Ais invertible. O D. Q=R 'A So y = , which shows that y is in Col A. AQx = A(Qx) R-Ax = (R-'A)x AR x=A (R 'x) AR x = (AR 1)x Click to %3D


Extracted text: Suppose A = QR where R is an invertible matrix, Show that and Q have the same column space. [Hint: Given y in Col A, show that y = Qx for some x. Also, given y in Col Q, show that y = Ax for some x.] If y is in Col A, then which of these is true? O A. y= QR. O B. y is in Col R. O C. x= Ay for some x. O D. y= Ax for some x. Then y = which shows that y is a linear combination of the columns of Q using the entries in Rx as weights. Therefore, y belongs to Col Q. Converse Col Q. Then y = Qx for some x. Since R is invertible, what does the equation A = QR imply? O A. Q QRx = (QR)x O B. A QRx = Q(Rx) O c. A O D. Q xQR = (xQ)R So y = xQR = x(QR) ch shows that y is in Col A.