You & maths

Exercise Set 1.1 – No. 4

4. Write down the augmented matrix for each of the linear systems in Exercise Set 1.1 – Number 3.

a) The augmented matrix of the system:

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

where x1, x2 of problem 3a is

$\large&space;{\color{Blue}&space;\begin{bmatrix}&space;a_{11}&space;&&space;a_{12}&space;&&space;b_1\\&space;a_{21}&space;&&space;a_{22}&space;&&space;b_2&space;\end{bmatrix}&space;}$

b) The augmented matrix of the system:

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

of problem 3b is

$\large&space;{\color{Blue}&space;\begin{bmatrix}&space;a_{11}&space;&&space;a_{12}&space;&&space;a_{13}&space;&&space;b_1\\&space;a_{21}&space;&&space;a_{22}&space;&&space;a_{23}&space;&&space;b_2\\&space;a_{31}&space;&&space;a_{32}&space;&&space;a_{33}&space;&&space;b_3&space;\end{bmatrix}&space;}$

c) The augmented matrix of the system:

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

of problem 3c is

$\large&space;{\color{Blue}&space;\begin{bmatrix}&space;a_{11}&space;&&space;a_{12}&space;&&space;a_{13}&space;&&space;a_{14}&space;&&space;b_1\\&space;a_{21}&space;&&space;a_{22}&space;&&space;a_{23}&space;&&space;a_{24}&space;&&space;b_2&space;\end{bmatrix}&space;}$