Mathematical Economics 29.1.2026

1.In a metric space, a set is open if:

• It contains all its limit points

• Every point has a neighborhood contained within the set

• It contains none of its limit points

• Every point has a neighborhood contained within the set

2.The determinant of a square matrix is zero if and only if:

• The matrix has an inverse

• The matrix is singular

• The matrix is diagonal

3.Cramer’s Rule is used to solve:

• Non-linear equations

• Systems of linear equations

• Differential equations

4.A set is called (a)   if it contains all its limit points.

5.In a metric space, a sequence is said to (a)   if its terms get arbitrarily close to some fixed point.

6.The inverse of a (a)   matrix exists only if its determinant is nonzero.

7.Every open set in a metric space is also closed.

• True

• False

8.In a system of linear equations, if the determinant of the coefficient matrix is zero, Cramer’s Rule cannot be applied.

• True

• False

9.Two matrices are equal if and only if they have the same dimensions and corresponding elements are equal.

• True

• False

10.The rank of a matrix is always greater than its number of rows.

• True

• False