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Study Guides > College Algebra

Solutions

Solutions to Try Its

1. [latex]\left[\begin{array}{cc}4& -3\\ 3& 2\end{array}|\begin{array}{c}11\\ 4\end{array}\right][/latex] 2. [latex]\begin{array}{c}x-y+z=5\\ 2x-y+3z=1\\ y+z=-9\end{array}[/latex] 3. [latex]\left(2,1\right)[/latex] 4. [latex]\left[\begin{array}{ccc}1& -\frac{5}{2}& \frac{5}{2}\\ \text{ }0& 1& 5\\ 0& 0& 1\end{array}|\begin{array}{c}\frac{17}{2}\\ 9\\ 2\end{array}\right][/latex] 5. [latex]\left(1,1,1\right)[/latex] 6. $150,000 at 7%, $750,000 at 8%, $600,000 at 10%

Solutions to Odd-Numbered Exercises

1. Yes. For each row, the coefficients of the variables are written across the corresponding row, and a vertical bar is placed; then the constants are placed to the right of the vertical bar. 3. No, there are numerous correct methods of using row operations on a matrix. Two possible ways are the following: (1) Interchange rows 1 and 2. Then [latex]{R}_{2}={R}_{2}-9{R}_{1}[/latex]. (2) [latex]{R}_{2}={R}_{1}-9{R}_{2}[/latex]. Then divide row 1 by 9. 5. No. A matrix with 0 entries for an entire row would have either zero or infinitely many solutions. 7. [latex]\left[\begin{array}{rrrr}\hfill 0& \hfill & \hfill 16& \hfill \\ \hfill 9& \hfill & \hfill -1& \hfill \end{array}|\begin{array}{rr}\hfill & \hfill 4\\ \hfill & \hfill 2\end{array}\right][/latex] 9. [latex]\left[\begin{array}{rrrrrr}\hfill 1& \hfill & \hfill 5& \hfill & \hfill 8& \hfill \\ \hfill 12& \hfill & \hfill 3& \hfill & \hfill 0& \hfill \\ \hfill 3& \hfill & \hfill 4& \hfill & \hfill 9& \hfill \end{array}|\begin{array}{rr}\hfill & \hfill 16\\ \hfill & \hfill 4\\ \hfill & \hfill -7\end{array}\right][/latex] 11. [latex]\begin{array}{l}-2x+5y=5\\ 6x - 18y=26\end{array}[/latex] 13. [latex]\begin{array}{l}3x+2y=13\\ -x - 9y+4z=53\\ 8x+5y+7z=80\end{array}[/latex] 15. [latex]\begin{array}{l}4x+5y - 2z=12\hfill \\ \text{ }y+58z=2\hfill \\ 8x+7y - 3z=-5\hfill \end{array}[/latex] 17. No solutions 19. [latex]\left(-1,-2\right)[/latex] 21. [latex]\left(6,7\right)[/latex] 23. [latex]\left(3,2\right)[/latex] 25. [latex]\left(\frac{1}{5},\frac{1}{2}\right)[/latex] 27. [latex]\left(x,\frac{4}{15}\left(5x+1\right)\right)[/latex] 29. [latex]\left(3,4\right)[/latex] 31. [latex]\left(\frac{196}{39},-\frac{5}{13}\right)[/latex] 33. [latex]\left(31,-42,87\right)[/latex] 35. [latex]\left(\frac{21}{40},\frac{1}{20},\frac{9}{8}\right)[/latex] 37. [latex]\left(\frac{18}{13},\frac{15}{13},-\frac{15}{13}\right)[/latex] 39. [latex]\left(x,y,\frac{1}{2}\left(1 - 2x - 3y\right)\right)[/latex] 41. [latex]\left(x,-\frac{x}{2},-1\right)[/latex] 43. [latex]\left(125,-25,0\right)[/latex] 45. [latex]\left(8,1,-2\right)[/latex] 47. [latex]\left(1,2,3\right)[/latex] 49. [latex]\left(x,\frac{31}{28}-\frac{3x}{4},\frac{1}{28}\left(-7x - 3\right)\right)[/latex] 51. No solutions exist. 53. 860 red velvet, 1,340 chocolate 55. 4% for account 1, 6% for account 2 57. $126 59. Banana was 3%, pumpkin was 7%, and rocky road was 2% 61. 100 almonds, 200 cashews, 600 pistachios

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