Linear Algebra, Analytic and Diferential Geometry

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Domeniu: Electrotehnică
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Cost: Gratis
Profesor îndrumător / Prezentat Profesorului: Conf. Dr. Calin C
Acesta este un curs in limba engleza.

Extras din document

1 Introduction to systems of linear

equations

Basic terminology

Methods of solving linear systems

2 Linear equations

Recall that in two dimensions a line in the rectangular

xOy−coordinate system can be represented by an equation

of the form

ax + by = c (a and b not both 0)

and in three dimensions a plane in a rectangular xyz−coordinate

system can be represented by an equation of the form

ax + by + cz = d (a, b, c not all 0).

More generally, we define a linear equation in n variables

x1, x2, ..., xn to be one that can be expressed in the form

a1x1 + a2x2 + ... + anxn = b

where a1, a2, ..., an and b are constants, and the a’s are

not all zero.

Example 1 4x1 − 5x2 + 2 = x1

rearranged

3x1 − 5x2 = −2

or

x2 = 2

³√6 − x1

´

+ x3

rearranged

2x1 + x2 − x3 = 2√6

Example 2 Not linear equation

4x1 − 5x2 + 2 = x1x2 or 4x1 − 5√x2 + 2 = 0

sin x1 + x2 = 0

Observe that in a linear equation all the variables occur

only to the first power and do not appear, for example,

as arguments of trigonometric, logarithmic or exponential

function.

Definition 3 The variables x1, x2, ..., xn are called unknowns.

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