You & maths

# Exercise Set 1.1 – No. 3

3. Using the notation of Formula:

$\large&space;{\color{Blue}&space;\begin{matrix}&space;a_{11}x_1&space;\:&space;+&space;\:&space;a_{12}x_2&space;\:&space;+&space;\:&space;...&space;\:&space;+&space;\:&space;a_{1n}x_n&space;\:=&space;b_1&space;\\&space;a_{21}x_1&space;\:&space;+&space;\:&space;a_{22}x_2&space;\:&space;+&space;\:&space;...&space;\:&space;+&space;\:&space;a_{2n}x_n&space;\:=&space;b_2&space;\\&space;\;&space;\;&space;\vdots&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\vdots&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\vdots&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\;&space;\vdots&space;\\&space;\:&space;\:&space;a_{m1}x_1&space;\:&space;+&space;\:&space;a_{m2}x_2&space;\:&space;+&space;\:&space;...&space;\:&space;+&space;\:&space;a_{mn}x_n&space;=&space;b_m&space;\\&space;\end{matrix}&space;}$

Write down a general linear system of

a) two equations in two unknowns.

b) three equations in three unknowns.

c) two equations in four unknowns.

a) A general linear system of two equations in two unknowns can be written
as:

$\large&space;{\color{blue}\begin{matrix}&space;a_{11}x_1&space;\:&space;+&space;\:&space;a_{12}x_2&space;=&space;b_1&space;\\&space;a_{21}x_1&space;\:&space;+&space;\:&space;a_{22}x_2&space;=&space;b_2&space;\\&space;\end{matrix}&space;}$

where x1 and x2 are the unknowns.

b) A general linear system of three equations in three unknowns can be written
as:

$\large&space;{\color{blue}\begin{matrix}&space;a_{11}x_1&space;\:&space;+&space;\:&space;a_{12}x_2&space;+&space;\:&space;a_{13}x_3=&space;b_1&space;\\&space;a_{21}x_1&space;\:&space;+&space;\:&space;a_{22}x_2&space;+&space;\:&space;a_{23}x_3=&space;b_2&space;\\&space;a_{31}x_1&space;\:&space;+&space;\:&space;a_{32}x_2&space;+&space;\:&space;a_{33}x_3=&space;b_3&space;\\&space;\end{matrix}&space;}$

where x1, x2 and x3 are the unknowns.

c) A general linear system of two equations in four unknowns can be written as:

$\large&space;{\color{blue}\begin{matrix}&space;a_{11}x_1&space;\:&space;+&space;\:&space;a_{12}x_2&space;+&space;\:&space;a_{13}x_3&space;+&space;\:&space;a_{14}x_4=&space;b_1&space;\\&space;a_{21}x_1&space;\:&space;+&space;\:&space;a_{22}x_2&space;+&space;\:&space;a_{23}x_3&space;+&space;\:&space;a_{24}x_4=&space;b_2&space;\\&space;\end{matrix}&space;}$

where x1, x2, x3 and x4 are the unknowns.