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 1O B. A=Q.OC. Ais invertible.O D. Q=R 'ASo y =, which shows that y is in Col A.AQx = A(Qx)R-Ax = (R-'A)xAR x=A (R 'x)AR x = (AR 1)xClick to%3D Suppose A = QR where R is an invertible matrix, Show thatand 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.ConverseCol Q. Then y = Qx for some x. Since R is invertible, what does the equation A = QR imply?O A. QQRx = (QR)xO B. AQRx = Q(Rx)O c. AO D. QxQR = (xQ)RSo y =xQR = x(QR)ch shows that y is in Col A.

Name: Conversely, suppose y belongs to Col Q. Then y = Qx for some x. Since
Uploaded: 2024-03-20T06:47:08.000Z
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Description: 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 1O B. A=Q.OC. Ais invertible.O D. Q=R 'ASo y =, which shows that y is in Col A.AQx = A(Qx)R-Ax = (R-'A)xAR x=A (R 'x)