GEOMETRIC PROGRESSION
Asequenceinwhichtheratioofanytermtotheprecedingterm
isconstantiscalledanGeometricSequenceoranGeometricProgres
sion.
i.e. Whenasequencehasaconstantratiobetweensuccessiveterms
itiscalledanGeometricProgression(oftenabbreviatedtoGP).
The
Mathematics for Technicians 3
2012 Oct
Complex Numbers
A complex number is a number comprising a real number and an
imaginary number. It is in the form a + jb, where a and b are real
numbers and j is the standard imaginary unit, i.e. j = ( 1).
Sometimes a
VECTORS
Define a vector, 2-dimensional
A scalar quantity is a purely numerical quantity with a unit,
i. e. A scalar is a quantity that has size but no direction.
Examples of scalars are mass, length, time, volume, speed and
temperature. e.g. (1) $20;
(
VECTORS
1.
In ABC, AB = a, AC = b and M is the mid-point of AB. Find in
terms of a and b (a) AM, (b) MC, (c) CM.
2.
In OAB OA, OB and OC are the vectors a, b and c respectively.
D is the mid-point of AB and E lies on BC extended such that BE
= 2BC. Find i
Using Gauss-Jordan
to Solve a System of Three Linear Equations
www.youtube.com/watch?v=CsTOUbeMPUo
This method involves transformation of a matrix, using row operations, to
obtain the identity matrix. The row operations are the operations used in
solving
Mathematics for Technicians 3
Complex Numbers
2012 Oct
Let a complex number be x + jy, as shown in the Argand diagram. From
trigonometry,
x = r cos
and
y = r sin .
x + jy
= r cos + j r sin
= r (cos + j sin )
= r (an abbreviation)
r is
Gaussian Elimination
Example
The augmented matrix for the system of equations
2x1 + x2 + 3x3 = 1
4x1 + 5x2 + 7x3 = 7
2x1 5x2 + 5x3 = 7
is
2 1 3 1
4 5 7 7
2 5 5 7
Ordinary arithmetic errors are a big problem when you do
row operations by hand. There is a
PRACTICE QUESTIONS ON
THREE-DIMENSIONAL VECTORS
1.
Calculate the cross product, A x B, given that
A = i 2j 3k
and
B = 3i j 2k.
10
2.
If the vector ti + 9j 4k is perpendicular to vector 3ti 4j + 3k,
calculate
the value(s) of t.
10
3. Th
MATRICES
Definition
Types of Matrices
Operations of Matrices
Row Echelon & Reduced Echelon Forms
Algebra of Matrices
Inverses of Matrices
Matrix Equations
DEFINITION
An m x n matrix is a rectangular array of numbers with m rows
and n columns.
DESCR