# Science:Math Exam Resources/Courses/MATH152/April 2012/Question 06 (d)

MATH152 April 2012
Other MATH152 Exams

### Question 06 (d)

This question requires little or no calculations.

Consider a linear system of 3 equations with 5 unknowns. Answer True or False to each of the following statements (no justification required).

(1) It always has at least one solution.

(2) There is either no solution or infinitely many solutions.

(3) If a solution exists, then there is precisely a 2-parameter family of solutions.

(4) If the coefficient matrix has rank k, then the associated homogeneous system as a k-parameter family of solutions.

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