Question

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

Answer 1

Answer:

True

Step-by-step explanation:

A linear system of equations will have a unique solution if and only if the number of variables equal the number of independent equations.

By independent equations we mean the same equation not repeated by multiplying by any constant.

Suppose number of variables are n, we must have the determinant formed by the coefficients non zero to have a unique solutions.

Here the no of equations are less than the number of variables.  So we cannot have a unique solution but can have a parametric solution using the number of parameters as n-m where n = number of variables and m = the number of independent equations given.

So the given statement is true.