In the Schaum's Outline to Liinear Algebra (p 47) the following
question is posed:
Let A =
[ 1 3 ]
[ 4 -3 ]
Find a nonzero colum vector u =
[ x ]
[ y ]
such that Au = 3u.
The book shows how the equations are to be set out and how they reduce
to 2x - 3y = 0.
It then comments as follows:
"The system reduces to one nondegenerate linear equation in two
unknowns, and so has an infinite number of solutions. To obtain a
nonzero solution, let, say, y = 2, then x = 3. Thus, u = (3,2)^T is a
desired nonzero vector.
To find the general solution, set y = a, where a is a parameter.
Substitute y = a into 2x - 3y = 0 to obtain x = (3/2)a. Thus, u =
(3/2a, a)^T represents all solutions.
What does the superscript T (^T) stand for? It doesn't seem as though
it can be the trace or transpose.
Many thanks in advance for help on a 3-day weekend.
Henrysun909
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