Question

6. What is the minimal length least-squares solution x*)= Atb to the following? (10 och 507 Ax = 1 0 0 0 = 2 .(20%) 1 1 1 Tele-2): 2009

Answer 1

Calculate the multiplication of transpose of A with matrix A. [1 1 1]1 0 o] [1+1+1 A A = 0 0 11 0 0= 0+0+1 0+0+1 0+0+1] [3 1 1] 0+0+1 0+0+1 =1 1 1 0+0+1 0+0+1 0+0+1 Calculate the multiplication of transpose of A with matrix b. [0+2+2] [1 1 1]0 Ab=0 0 1 2 =0+0+2 %3D 0 0 1|| 2 0+0+2 2

Find the solution using minimal length least squares solution. [A A] d =[A*b] %3D 3 1 1 1 1 1 |1 1 1 | 2 3 1 14 1 1 12 1 1 12 [12+2+2 4+2+2 4+2+2 [16 =c=16, d = 8, e= 8 2.