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Study Guides > MATH 1314: College Algebra

Solutions

Solutions to Try Its

1. [4332114]\left[\begin{array}{cc}4& -3\\ 3& 2\end{array}|\begin{array}{c}11\\ 4\end{array}\right] 2. xy+z=52xy+3z=1y+z=9\begin{array}{c}x-y+z=5\\ 2x-y+3z=1\\ y+z=-9\end{array} 3. (2,1)\left(2,1\right) 4. [15252 01500117292]\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] 5. (1,1,1)\left(1,1,1\right) 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 R2=R29R1{R}_{2}={R}_{2}-9{R}_{1}. (2) R2=R19R2{R}_{2}={R}_{1}-9{R}_{2}. 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. [0169142]\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] 9. [15812303491647]\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] 11. 2x+5y=56x18y=26\begin{array}{l}-2x+5y=5\\ 6x - 18y=26\end{array} 13. 3x+2y=13x9y+4z=538x+5y+7z=80\begin{array}{l}3x+2y=13\\ -x - 9y+4z=53\\ 8x+5y+7z=80\end{array} 15. 4x+5y2z=12 y+58z=28x+7y3z=5\begin{array}{l}4x+5y - 2z=12\hfill \\ \text{ }y+58z=2\hfill \\ 8x+7y - 3z=-5\hfill \end{array} 17. No solutions 19. (1,2)\left(-1,-2\right) 21. (6,7)\left(6,7\right) 23. (3,2)\left(3,2\right) 25. (15,12)\left(\frac{1}{5},\frac{1}{2}\right) 27. (x,415(5x+1))\left(x,\frac{4}{15}\left(5x+1\right)\right) 29. (3,4)\left(3,4\right) 31. (19639,513)\left(\frac{196}{39},-\frac{5}{13}\right) 33. (31,42,87)\left(31,-42,87\right) 35. (2140,120,98)\left(\frac{21}{40},\frac{1}{20},\frac{9}{8}\right) 37. (1813,1513,1513)\left(\frac{18}{13},\frac{15}{13},-\frac{15}{13}\right) 39. (x,y,12(12x3y))\left(x,y,\frac{1}{2}\left(1 - 2x - 3y\right)\right) 41. (x,x2,1)\left(x,-\frac{x}{2},-1\right) 43. (125,25,0)\left(125,-25,0\right) 45. (8,1,2)\left(8,1,-2\right) 47. (1,2,3)\left(1,2,3\right) 49. (x,31283x4,128(7x3))\left(x,\frac{31}{28}-\frac{3x}{4},\frac{1}{28}\left(-7x - 3\right)\right) 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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