Practice questions

Various practice questions will be posted here as the semester progresses. These questions are from previous exams, assignments and tutorials. No solutions will be posted.

Tutorial 3, 2009

• Convert into decimal representation: (a) $(10011101{)}_2$; (b) $(0.001101{)}_2$
• Convert into binary representation: (a) $(45.625{)}_{10}$; (b) $(0.1{)}_{10}$
• Consider the following system of linear algebraic equations.
  • Use Gauss elimination (without pivoting) to solve these equations for $(x_1,x_2,x_3)$.
  • Validate your solution by comparing it to the one obtained with computer software.

$$\begin{array}{r}\{\begin{array}{rcl}2x_1-2x_2+4x_3& =& 0\\ x_1-3x_2+4x_3& =& -1\\ 3x_1-x_2+5x_3& =& 0\end{array}\end{array}$$

Tutorial 4, 2009

• We have already seen several elimination techniques for linear equation solving. In this question, you are to solve the following linear algebraic equations, using LU decomposition

$$\begin{array}{r}\{\begin{array}{rcl}2x_1-2x_2+4x_3& =& 0\\ x_1-3x_2+4x_3& =& -1\\ 3x_1-x_2+5x_3& =& 0\end{array}\end{array}$$

• We have also seen that the LU decomposition technique can be used to calculate matrix inverses. Using the results obtained in the question above, compute the inverse of the following matrix,

$$\begin{array}{rl}A& =\left[\begin{array}{rrr}2& -2& 4\\ 1& -3& 4\\ 3& -1& 5\end{array}\right]\end{array}$$