MAM2000W 2LA NOTES

Linear
Algebra

,
, DEFINITION: Let A be an matrix,

A scalar is called an A if there is

vector "x" Such that : Such a vector x is called an

* corresponding to



EXAMPLE : Show that [27 an


A: 3 to
correspanding



SOLUTION: 3




-


3.2 +

3.2 +




of correspanding to
is an
the Cigenvalue
1a 4

, How To FIND EIGENVALLES/VECTORS


To Solve for the eigenvalues 1 Ai , and the

at an matrix A elo the

0 Multiply an
identity_ matrix by the Scalar, 2.


i Subtract the
identity matrix multiple from the matms A
0:

0 Find the determinaot of the matrix difference
and the




0 Solve for the volues of 1 (hat the equatign
det CA- RI= o




5) Solve the
corresponding vector to each 2.


Find the eigenvalues and of the matrix




Solution : 21:




A - AI=