3 Determinants
3.1 Introduction to Determinants
Recallthatif' b
' O.
A~lc all
det (A) = as! be.
We showed that A1 exists i det (A) # 0. For general 73 x n matrices, there is
a similar number det (A) that has the same property. It can be derived using
MATH1502 - Homework 3 - due April 10, 2012
March 6 Version
Name _
Group (e.g. C1 or G1 or M1) _
Student Number_
Teaching Assistant_
Question Number
Points
Total
Question 1
Solve, if possible the system of linear equations
x1 + x2 + 2 x3 = 7
x1 + 5x2 + 8x3
5 Eigenvalues and Eigenvectors
5.1 Eigenvectors and Eigenvalues
I {-5.2 The Characteristic Equation -
Denition: Eigenvalues and Eigenvectors
Let A be an n x 71 matrix. A number A is called an eigenvalue 'of A if there
is a nonzero vector x such that
Ax =