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Chapter 1: Q30E (page 1)

Give an example of an inconsistent underdetermined system of two equations in three unknowns.

Short Answer

Expert verified

One of the examples of an inconsistent underdetermined system of two equations in three unknowns is

Step by step solution

01

Inconsistent underdetermined system

The underdetermined system is a system of equations with fewer equations than unknowns. When this system becomes inconsistent, it is known as an inconsistent underdetermined system.

02

Consider the example

Consider the system of two equations in three unknowns, that is, an underdetermined system:

\(\begin{array}{c}x + 2y + z = 2\\ - x - 2y - z = 1\end{array}\)

03

Apply the addition operator

Add the above two equations to get:

\(0 = 3\)

This is not possible. So, our system is inconsistent.

04

Conclusion

Hence, the system given below is an example of an inconsistent underdetermined system of two equations in three unknowns.

\(\begin{array}{c}x + 2y + z = 2\\ - x - 2y - z = 1\end{array}\)

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