Three steps to compute A x

Here's the picture of xA x for another 2 × 2 matrix A

You see that A(u_1 + u_2) = 3v_1 + 2v_2.  Your job is to compute A x .

(Q16)  The singular values of A are __ and __.

Three steps to compute A x .

Step 1:  Find the u_i coordinates for x .  
    You see x = 1.5u_1 + 2u_2.
Step 2:  Multiply the u_i coordinates by the singular values.      
     3 (1.5) = 4.5 and 2 (2) = 4.
Step 3:  Use these numbers as v_i coordinates of A x.
    A x = 4.5v_1 + 4v_2.

Carry out the three steps to compute A w .

(Q17) Step 1, find the u_i coords for w : w = __ u_1 + __ u_2.

Step 2, multiply the u_i coords by the singular values.

(Q18) Step 3, use these numbers as v-coords for A w : A w = __ v_1 + __ v_2.

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Copyright © 2007 Todd Will
Created by Mathematica  (April 15, 2007)