Find the QR decomposition of the matrix Find the QR decompos

Find the QR decomposition of the matrix:

Find the QR decomposition of the matrix: A = -1 2 1 -1 1 -4 1 4- 3 1-4 7 1 2 1

Solution

A should be equal to QR

a1 = (-1, -1, 1 , 1, 1) = u1

e1 = u1 / det u1 = (-0.447, -0.447, 0.447, 0.447, 0.447)

u2 = a2 - (a2.e1) e1

  u2 = ( 9/5, 4/5, 21/5, -19/5, 11/5)

e2 = u2 / det u2 = ( 0.281, 0.125, 0.657, -0.5949, 0.3444)

u3 = a3 - (a3.e1)e1 - (a3.e2)e2

u3 = (4.276, -1.66, -0.648, 1.841, 1.47)

e3 = (0.822, -0.319, -0.124, 0.354, 0.282)

Q = (e1   e2    e3)

Q = ( -0.447 0.281   0.822

          -0.447   0.125   -0.319

           0.447    0.657    -0.124

          0.447     -0.594   0.354

         0.447     0.344      0.282)

R = ( 2.235      -0.447     3.576

         0             6.383       -6

         0                0           5.23 )

The above QR form the decomposition of the matrix