1.\u00a0[latex]\\left[\\begin{array}{cc}4& -3\\\\ 3& 2\\end{array}|\\begin{array}{c}11\\\\ 4\\end{array}\\right][\/latex]<\/p>\n
2.\u00a0[latex]\\begin{array}{c}x-y+z=5\\\\ 2x-y+3z=1\\\\ y+z=-9\\end{array}[\/latex]<\/p>\n
3.\u00a0[latex]\\left(2,1\\right)[\/latex]<\/p>\n
4.\u00a0[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]<\/p>\n
5.\u00a0[latex]\\left(1,1,1\\right)[\/latex]<\/p>\n
6.\u00a0$150,000 at 7%, $750,000 at 8%, $600,000 at 10%<\/p>\n
1.\u00a0Yes. 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.<\/p>\n
3.\u00a0No, 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.<\/p>\n
5.\u00a0No. A matrix with 0 entries for an entire row would have either zero or infinitely many solutions.<\/p>\n
7.\u00a0[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]<\/p>\n
9.\u00a0[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]<\/p>\n
11.\u00a0[latex]\\begin{array}{l}-2x+5y=5\\\\ 6x - 18y=26\\end{array}[\/latex]<\/p>\n
13.\u00a0[latex]\\begin{array}{l}3x+2y=13\\\\ -x - 9y+4z=53\\\\ 8x+5y+7z=80\\end{array}[\/latex]<\/p>\n
15.\u00a0[latex]\\begin{array}{l}4x+5y - 2z=12\\hfill \\\\ \\text{ }y+58z=2\\hfill \\\\ 8x+7y - 3z=-5\\hfill \\end{array}[\/latex]<\/p>\n
17.\u00a0No solutions<\/p>\n
19.\u00a0[latex]\\left(-1,-2\\right)[\/latex]<\/p>\n
21.\u00a0[latex]\\left(6,7\\right)[\/latex]<\/p>\n
23.\u00a0[latex]\\left(3,2\\right)[\/latex]<\/p>\n
25.\u00a0[latex]\\left(\\frac{1}{5},\\frac{1}{2}\\right)[\/latex]<\/p>\n
27.\u00a0[latex]\\left(x,\\frac{4}{15}\\left(5x+1\\right)\\right)[\/latex]<\/p>\n
29.\u00a0[latex]\\left(3,4\\right)[\/latex]<\/p>\n
31.\u00a0[latex]\\left(\\frac{196}{39},-\\frac{5}{13}\\right)[\/latex]<\/p>\n
33.\u00a0[latex]\\left(31,-42,87\\right)[\/latex]<\/p>\n
35.\u00a0[latex]\\left(\\frac{21}{40},\\frac{1}{20},\\frac{9}{8}\\right)[\/latex]<\/p>\n
37.\u00a0[latex]\\left(\\frac{18}{13},\\frac{15}{13},-\\frac{15}{13}\\right)[\/latex]<\/p>\n
39.\u00a0[latex]\\left(x,y,\\frac{1}{2}\\left(1 - 2x - 3y\\right)\\right)[\/latex]<\/p>\n
41.\u00a0[latex]\\left(x,-\\frac{x}{2},-1\\right)[\/latex]<\/p>\n
43.\u00a0[latex]\\left(125,-25,0\\right)[\/latex]<\/p>\n
45.\u00a0[latex]\\left(8,1,-2\\right)[\/latex]<\/p>\n
47.\u00a0[latex]\\left(1,2,3\\right)[\/latex]<\/p>\n
49.\u00a0[latex]\\left(x,\\frac{31}{28}-\\frac{3x}{4},\\frac{1}{28}\\left(-7x - 3\\right)\\right)[\/latex]<\/p>\n
51.\u00a0No solutions exist.<\/p>\n
53.\u00a0860 red velvet, 1,340 chocolate<\/p>\n
55.\u00a04% for account 1, 6% for account 2<\/p>\n
57.\u00a0$126<\/p>\n
59.\u00a0Banana was 3%, pumpkin was 7%, and rocky road was 2%<\/p>\n
61.\u00a0100 almonds, 200 cashews, 600 pistachios<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t