Question

16. Given a system of m simultaneous linear equations in n unknowns (m<n), the number of basic variables will be
(a) m.
(c) n-m,
(b) n,
(d) n + m.​

Answer 1

Step-by-step explanation:

Theorem 1 Given a system of m equations in n unknowns: If m<n then the number of parameters in the solution will be at least n − m. (Thus if there is a unique solution we must have m ≥ n.) If m>n the system is called overprescribed.

Answer 2

Given,

Number of linear equations $\[ = m\]$

Number of unknowns $\[ = n\]$

Solution,

Number of basic variables,

= Number of unknown - Number of linear equations

$\[ = n - m\]$

Hence the basic variable will be $\[ n - m\]$

The correct option is (c), i.e. $\[ n - m\]$.