MATH 2318.1P1
TEST 2
PAGE 1
Theorems and Formulas
Theorem 3.1.1
If u, v, and w be vectors in 8 , and if 5 and 7 are scalars, then:
(a)
uvvu
(b)
(c)
u 0 0 u u.
(d)
(e)
5 u v 5 u 5 v
(f)
(g)
5 7 u 57 u
u v w u v w
u u 0
5 7 u 5 u 7 u
(h)
"u u
Theorem 3.1.2
MATH 2318.1P1
TEST 3
PAGE 1
Theorems and Formulas
Definition 5.1.1
If E is an 8 8 matrix, then a nonzero vector x in 8 is called an eigenvector of E (or of the matrix operator XE ) if
Ex is a scalar multiple of x; that is Ex -x for some scalar - . The sca
MATH 2318.1P1
TEST 1 - ARDIS
PAGE 10
Theorems and Formulas
Theorem 1.4.6 The Inverse of a Product
If E and F are inevitable matrices with the same size, then EF is invertible and EF" F " E" .
Theorem 1.4.6 Properties of an Inverse Matrix
If E is invertibl