The 'T' means transposed.

Consider the four non-zero COLUMN vectors in R^2:

x=[x1, x2]; y=[y1, y2]; w=[w1, w2]; z=[z1, z2]

Let xTw=0, yTz=0, A=xyT, B=wzT

Determine:

a) The 2-norm of A

b) The singular value decomposition (SVD) of A

c) The Range space and Nullspace of A

d) The pseudo-inverse de A

e) The singular value decomposition (SVD) of A+B