Question

T67 [21] (1 point) Let A = 1 1 and b = [21] -6 .The QR factorization of the matrix A is given by: 1-3] [21] [ 11 = [2 1 112] 2 -V2 ماده و V2 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. 5/3 -3

Answer 1

Solution Ceiven Α- ι and b= and QR factorization of the matn's A is given تير 2,73 LBL 2 1 Globate م می the least spare (a) Apply the QR fautorization to solve problem Ax= We Apply the method as 6.?Q?Q=1 ) Ax=b QR z = b Ra = QTb = Rx = The final systew Rx = Qb is folve as Ax=b Q Razb is triangular and its coefficient بر اين pler اي مانن ما أتم نانی حلم مايم at win at - - PABLO 3XL

colo lo 9) w WINT kujac + (styveg 4 (1989) vos 2x) wlos L - LA - Anwen of parla Ansu 6 syster in part @ Use back substitution to Colve the and find the least square solter solve 2 above: (By back substitution M = -%2 => x = -37 34 + + 2 = 0 → 94 +3*1-21)-0 - 34 - 45 34 = 45 X = Aurr