Section 3.3

1. $[\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]$ $[\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]$
2. $[\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]$ $[\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]$
3. $[\begin{array}{r} 1 & 0 & - 2 \\ 0 & 1 & 3 \end{array}]$ $[\begin{array}{r} 1 & 0 & - 2 \\ 0 & 1 & 3 \end{array}]$
4. $[\begin{array}{r} 1 & 0 & 2 \\ 0 & 1 & - 1 \end{array}]$ $[\begin{array}{r} 1 & 0 & 2 \\ 0 & 1 & - 1 \end{array}]$
5. $[\begin{array}{l} 1 & 0 & - 5 \\ 0 & 1 & - 3 \end{array}]$ $[\begin{array}{l} 1 & 0 & - 5 \\ 0 & 1 & - 3 \end{array}]$
6. $[\begin{array}{r} 1 & 0 & 7 \\ 0 & 1 & - 6 \end{array}]$ $[\begin{array}{r} 1 & 0 & 7 \\ 0 & 1 & - 6 \end{array}]$
7. $[\begin{array}{r} 1 & 0 & 5 \\ 0 & 1 & - 1 \\ 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 & 5 \\ 0 & 1 & - 1 \\ 0 & 0 & 0 \end{array}]$
8. $[\begin{array}{r} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$ $[\begin{array}{r} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$
9. $[\begin{array}{r} 1 & 0 & 2 \\ 0 & 1 & 4 \\ 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 & 2 \\ 0 & 1 & 4 \\ 0 & 0 & 0 \end{array}]$
10. $[\begin{array}{r} 1 & 0 & - 3 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 & - 3 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{array}]$
11. $[\begin{array}{r} 1 & 3 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 3 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}]$
12. $[\begin{array}{r} 1 & - 4 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & - 4 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}]$
13. $[\begin{array}{r} 1 & 0 & 0 & 3 \\ 0 & 1 & 0 & - 2 \\ 0 & 0 & 1 & 2 \end{array}]$ $[\begin{array}{r} 1 & 0 & 0 & 3 \\ 0 & 1 & 0 & - 2 \\ 0 & 0 & 1 & 2 \end{array}]$
14. $[\begin{array}{r} 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & - 3 \\ 0 & 0 & 1 & 5 \end{array}]$ $[\begin{array}{r} 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & - 3 \\ 0 & 0 & 1 & 5 \end{array}]$
15. $[\begin{array}{r} 1 & 0 & - 1 & 2 \\ 0 & 1 & 3 & - 1 \\ 0 & 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 & - 1 & 2 \\ 0 & 1 & 3 & - 1 \\ 0 & 0 & 0 & 0 \end{array}]$
16. $[\begin{array}{r} 1 & 0 & 3 & - 2 \\ 0 & 1 & 4 & 3 \\ 0 & 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 & 3 & - 2 \\ 0 & 1 & 4 & 3 \\ 0 & 0 & 0 & 0 \end{array}]$
17. $[\begin{array}{r} 1 & 0 & 0 & 2 & - 3 \\ 0 & 1 & 0 & - 1 & 4 \\ 0 & 0 & 1 & - 2 & - 5 \end{array}]$ $[\begin{array}{r} 1 & 0 & 0 & 2 & - 3 \\ 0 & 1 & 0 & - 1 & 4 \\ 0 & 0 & 1 & - 2 & - 5 \end{array}]$
18. $[\begin{array}{r} 1 & 0 & 3 & - 2 & 3 \\ 0 & 1 & 4 & 5 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 & 3 & - 2 & 3 \\ 0 & 1 & 4 & 5 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}]$
19. $[\begin{array}{r} 1 & 0 & 2 & 1 & 3 \\ 0 & 1 & - 2 & - 3 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 & 2 & 1 & 3 \\ 0 & 1 & - 2 & - 3 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}]$
20. $[\begin{array}{r} 1 & 2 & 0 & 2 & 3 \\ 0 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 2 & 0 & 2 & 3 \\ 0 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 \end{array}]$
21. $x_{1} = 3, x_{2} = - 2, x_{3} = 4$ $x_{1} = 3, x_{2} = - 2, x_{3} = 4$
22. $x_{1} = 5, x_{2} = - 3, x_{3} = 2$ $x_{1} = 5, x_{2} = - 3, x_{3} = 2$
23. $x_{1} = 4 + 3 t, x_{2} = 3 - 2 t, x_{3} = t$ $x_{1} = 4 + 3 t, x_{2} = 3 - 2 t, x_{3} = t$
24. $x_{1} = 5 + 2 t, x_{2} = t, x_{3} = 7$ $x_{1} = 5 + 2 t, x_{2} = t, x_{3} = 7$
25. Inconsistent—no solution
26. Inconsistent—no solution
27. $x_{1} = 3 - 2 t, x_{2} = - 4 + t, x_{3} = 5 - 3 t, x_{4} = t$ $x_{1} = 3 - 2 t, x_{2} = - 4 + t, x_{3} = 5 - 3 t, x_{4} = t$
28. $x_{1} = 4 + 2 s - 3 t, x_{2} = s, x_{3} = 3 - 4 t, x_{4} = t$ $x_{1} = 4 + 2 s - 3 t, x_{2} = s, x_{3} = 3 - 4 t, x_{4} = t$
29. $x_{1} = 3 - s - t, x_{2} = 5 + 2 s - 3 t, x_{3} = s, x_{4} = t$ $x_{1} = 3 - s - t, x_{2} = 5 + 2 s - 3 t, x_{3} = s, x_{4} = t$
30. $x_{1} = 2 + 3 t, x_{2} = 1 + s - 2 t, x_{3} = 2 + 2 s, x_{4} = s, x_{5} = t$ $x_{1} = 2 + 3 t, x_{2} = 1 + s - 2 t, x_{3} = 2 + 2 s, x_{4} = s, x_{5} = t$
31. The sequence $\frac{1}{6} R_{3}, R_{2} - 5 R_{3}, \frac{1}{4} R_{2}, R_{1} - 2 R_{2}, R_{1} - 3 R_{3}$ $\frac{1}{6} R_{3}, R_{2} - 5 R_{3}, \frac{1}{4} R_{2}, R_{1} - 2 R_{2}, R_{1} - 3 R_{3}$ of row operations transforms the first matrix to the identity matrix.
33. $[\begin{array}{r} 1 & 0 \\ 0 & 1 \end{array}], [\begin{array}{r} 1 & * \\ 0 & 0 \end{array}], [\begin{array}{l} 0 & 1 \\ 0 & 0 \end{array}], [\begin{array}{l} 0 & 0 \\ 0 & 0 \end{array}]$ $[\begin{array}{r} 1 & 0 \\ 0 & 1 \end{array}], [\begin{array}{r} 1 & * \\ 0 & 0 \end{array}], [\begin{array}{l} 0 & 1 \\ 0 & 0 \end{array}], [\begin{array}{l} 0 & 0 \\ 0 & 0 \end{array}]$

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Table of Contents for Section 3.3

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Table of Contents for
Section 3.3