Question

Materials covered: 1.1-1.5 Question 1: Give an example of a 3 x 3 matrix in row echelon form that represents for the following system characteristics: (a) In-consistent system. (b) Consistent system and has many solutions. (c) Consistent system and has a unique solution.

Answer 1

Explanation:

Consider the 3x3 matrices in row echelon form:

`\left[\begin{array}{ccc}1&2&0\\0&1&2\\0&0&0\end{array}\right]`

and

`\left[\begin{array}{ccc}1&2&0\\0&1&2\\0&0&1\end{array}\right]`

a) The augmented matrix

`\left[\begin{array}ccc1&2&0&1\\0&1&2&1\\0&0&0&2\end{array}\right]`

corresponds to an inconsistent system.

b) The augmented matrix

`\left[\begin{array}c1&2&0&1\\0&1&2&1\\0&0&0&0\end{array}\right]`

corresponds to a consistent system with infinite solutions.

(c) The augmented matrix

`\left[\begin{array}c1&2&0&1\\0&1&2&1\\0&0&1&1\end{array}\right]`

corresponds to a consistent system with infinite solutions.