Quiz 8

Date: MATH 1090-4 - Fall 2003

Note: Unless stated otherwise, answers without justification receive no credit. Please, show your work!

1. Let

   $$A=\left[ \begin{array}{ccc} 1 & -1 & 2\\ 4 & 0 & 1 \end{array} \right] \quad B=\left[ \begin{array}{cc} 0&1\\ 1&0 \end{array} \right]$$

   
   
   Perform each of the following computations or state why they can't be done.
   1. $2\cdot B + A\cdot (A^t)$.
   2. $2\cdot B + (A^t)\cdot A$.

2. Consider the system of equations

   $$\begin{cases}x+y-z=0\\ x+2y+3z=-5\\ 2x-y-13z=17. \end{cases}$$

   
   
   1. Write the augmented matrix of the system.
   2. Use Gauss-Jordan elimination to ``simplify'' the augmented matrix.
   3. Use the reduced matrix that you found above to solve the system of equations.
   4. According with your computations, how many solutions does the system have?