Q1: If \(A\) is a \(2 \times 2\) matrix, show that if \(AB = 0\) for all \(2 \times 1\) matrices B, then \(A = 0\).
Q2: Consider a \(4 \times 4\) diagonal matrix \(A\) with non-zero entries along the diagonal and suppose \(AB = I_{4}\). What would the matrix \(B\) be?
Q3: Solve the system of equations \(\begin{cases} x+y+z=1 \\ 2x+7y+3z=4 \\ x+6y+z+2=0 \end{cases}\).
Q4: For what values of \(a\) and \(b\) allows the following system of equations to have 1) one (unique) solution 2) no solutions: \(\begin{cases} x + 0 = 3 \\ by = a \end{cases}\).
