Question

Use a software program or a graphing utility with matrix capabilities to find the transition matrix from B to B'.

B = {(2, 5), (1, 2)}, B' = {(2, −5), (−1, 5)}

Answer 1

Let A =

2	-1	2	1
-5	5	5	2

It may be observed that the columns of A are the vectors in B’ and B respectively.

To determine the transition matrix from B to B', we will reduce A to its RREF, as under, by using the software program available at http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref.

Multiply the 1st row by ½

Add 5 times the 1st row to the 2nd row

Multiply the 2nd row by 2/5

Add 1/2 times the 2nd row to the 1st row

Then the RREF of A is

1	0	3	7/5
0	1	4	9/5

Hence, the transition matrix from B to B' is M(say) =

3	7/5
4	9/5