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

where x1, x2 of problem 3a is

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

b) The augmented matrix of the system:

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

of problem 3b is

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

c) The augmented matrix of the system:

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

of problem 3c is

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