Online quiz (due Wednesday 17th May, 11:59pm):

Answer all five questions. Each question is worth 2 marks, the total is 10 marks.

• – SOLVE 1

  Find the solution to the following system of linear equations:

  • There are infinitely many solutions

  • $x=-\frac{11}{4},y=-\frac{7}{4},z=\frac{25}{4}$,

  • $x=3,y=2,z=7$,

  • $x=\frac{11}{4},y=\frac{7}{4},z=\frac{25}{4}$,

  • None of the above.

• – SOLVE 2

  Find the solution to the following system of linear equations:

  • The unique solution is $(x,y,z)=\frac{1}{7}(5,3,0)$,

  • The unique solution is $(x,y,z)=\frac{1}{7}(5,-3,0)$,

  • There are infinitely many solutions:

    $$\left\{\left(\begin{array}{c}\hfill x\hfill \\ \hfill y\hfill \\ \hfill z\hfill \end{array}\right)=\frac{1}{7}\left(\begin{array}{c}\hfill 5\hfill \\ \hfill 3\hfill \\ \hfill 0\hfill \end{array}\right)+\zeta \left(\begin{array}{c}\hfill 1\hfill \\ \hfill 5\hfill \\ \hfill -7\hfill \end{array}\right)\mathit{\hspace{1em}}\text{,}\mathit{\hspace{1em}}\zeta \in ℝ\right\},$$

  • There are infinitely many solutions:

    $$\left\{\left(\begin{array}{c}\hfill x\hfill \\ \hfill y\hfill \\ \hfill z\hfill \end{array}\right)=\frac{1}{7}\left(\begin{array}{c}\hfill 5\hfill \\ \hfill -3\hfill \\ \hfill 0\hfill \end{array}\right)+\zeta \left(\begin{array}{c}\hfill 1\hfill \\ \hfill 5\hfill \\ \hfill 7\hfill \end{array}\right)\mathit{\hspace{1em}}\text{,}\mathit{\hspace{1em}}\zeta \in ℝ\right\},$$

  • None of the above.

• – CONVERT 1

  Which matrix could be the augmented matrix of the following system of equations

  • None of the above.

• – CONVERT 2

  Which of these systems of linear equations does the following augmented matrix represent?

  • All of the above

  • None of the above.

• – PARAMETERS

  For which values of $\lambda$ and $\mu$ does the following system of linear equations (with variables $x,y,$ and $z$) have a unique solution?

  • $\lambda \ne -7$ and $\mu \ne -9$,

  • $\lambda \ne 7$ and $\mu \ne 9$,

  • $\lambda \ne -7$ and $\mu$ can take any value,

  • $\lambda$ can take any value but $\mu \ne -9$,

  • the system is always inconsistent, for all values of $\lambda$ and $\mu$.

• – INVERTING A $5\times 5$ MATRIX

  Find the inverse of the matrix