Question

Determine if the statement is true or false. Any linear system with more variables than equations cannot have a unique solution.

Answer 1

Answer:

True

Step-by-step explanation:

Suppose a system contains a large number of variables than equations, then there is a need to make assumptions of some values for the extra variables in order to solve the system. So, the assigning of these values can be done in several ways. Thus, the system cannot contain a unique solution.

Also, for a system of the linear equation:

$AX = B$  can have a unique solution if:

Augmented matrix(rank) = coefficient matrix(rank) = no. of variables.

Provided that there exist fewer equations and more variables,

Then;

coefficient matrix(rank) <  no. of variables

Thus, the system cannot contain a unique solution.