Matrices and determinants

Calculate the determinant of the following matrix: \[ \left (\array{ \frac12 & 0 & -1\cr 2 & 1& 0\cr 1 & \frac12 & 2\cr } \right ) \]

Which of the given matrices \(A\), \(B\), \(C\) and \(D\) has a different determinant than the others? \[ A=\left (\array{ 6 & 11 \cr 2 & 2\cr } \right ) \] \[ B=\left (\array{ 1 & 3 \cr 5 & 2\cr } \right ) \] \[ C=\left (\array{ 5 & -2 \cr 10 & -6\cr } \right ) \] \[ D=\left (\array{ 10 & 0 \cr -7 & -1\cr } \right ) \]

Determine the set of all real numbers \(b\) for which the determinant of the following matrix equals to \(5\). \[ \left (\array{ 4 & b & -1\cr 3 &0& 2\cr b & 0 & -1\cr } \right ) \]

Calculate the determinant of the following matrix: \[ \left (\array{ 7 & 6 & 1\cr 3 & 2& 1\cr 2 & 7& -1\cr } \right ) \]