MA2007B Linear Algebra Homework 1

Under what condition on $y_{1}$ , $y_{2}$ , $y_{3}$ do the points $(0, y_{1})$ , $(1, y_{2})$ , $(2, y_{3})$ lie on a straight line?
Use elimination to solve

{\begin{cases} u + v + w = 6 \\ u + 2 v + 2 w = 11 \\ 2 u + 3 v - 4 w = 3 \end{cases}

and

{\begin{cases} u + v + w = 7 \\ u + 2 v + 2 w = 10 \\ 2 u + 3 v - 4 w = 3 \end{cases}

Prove the following statements:
1. Prove that if the determinant of the coefficient matrix for the following system of linear equations
  ${\begin{cases} a x + b y = k \\ c x + d y = l \end{cases}$
  is non-zero, then this system has a solution.
2. Prove that if a system of two linear equations with two unknowns has more than one solution, it must have infinitely many solutions.