1.1.8 Vector Algebra

Problem: Reduce the following matrix to a normal form by elementary transformations: \[ \left(\begin{array}{ccc} 3 \lambda^{2}-5 \lambda+2 & 0 & 3 \lambda^{2}-6 \lambda+3 \\ 2 \lambda^{2}-3 \lambda+1 & \lambda-1 & 2 \lambda^{2}-4 \lambda+2 \\ 2 \lambda^{2}-2 \lambda & 0 & 2 \lambda^{2}-4 \lambda+2 \end{array}\right) \]