System of Equations With Matrices: Get Stronger Answer Key

Introduction to Matrices and Matrix Operations

  1. [latex]\left[\begin{array}{cc}\hfill 11& \hfill 19\\ \hfill 15& \hfill 94\\ \hfill 17& \hfill 67\end{array}\right][/latex]
  2. [latex]\left[\begin{array}{cc}\hfill -4& \hfill 2\\ \hfill 8& \hfill 1\end{array}\right][/latex]
  3. Unidentified; dimensions do not match
  4. [latex]\left[\begin{array}{cc}\hfill 9& \hfill 27\\ \hfill 63& \hfill 36\\ \hfill 0& \hfill 192\end{array}\right][/latex]
  5. [latex]\left[\begin{array}{cccc}\hfill -64& \hfill -12& \hfill -28& \hfill -72\\ \hfill -360& \hfill -20& \hfill -12& \hfill -116\end{array}\right][/latex]
  6. [latex]\left[\begin{array}{ccc}\hfill 1,800& \hfill 1,200& \hfill 1,300\\ \hfill 800& \hfill 1,400& \hfill 600\\ \hfill 700& \hfill 400& \hfill 2,100\end{array}\right][/latex]
  7. [latex]\left[\begin{array}{cc}\hfill 20& \hfill 102\\ \hfill 28& \hfill 28\end{array}\right][/latex]
  8. [latex]\left[\begin{array}{ccc}\hfill 60& \hfill 41& \hfill 2\\ \hfill -16& \hfill 120& \hfill -216\end{array}\right][/latex]
  9. [latex]\left[\begin{array}{ccc}\hfill -68& \hfill 24& \hfill 136\\ \hfill -54& \hfill -12& \hfill 64\\ \hfill -57& \hfill 30& \hfill 128\end{array}\right][/latex]
  10. Undefined; dimensions do not match.
  11. [latex]\left[\begin{array}{ccc}\hfill -8& \hfill 41& \hfill -3\\ \hfill 40& \hfill -15& \hfill -14\\ \hfill 4& \hfill 27& \hfill 42\end{array}\right][/latex]
  12. [latex]\left[\begin{array}{ccc}\hfill -840& \hfill 650& \hfill -530\\ \hfill 330& \hfill 360& \hfill 250\\ \hfill -10& \hfill 900& \hfill 110\end{array}\right][/latex]
  13. [latex]\left[\begin{array}{cc}\hfill -350& \hfill 1,050\\ \hfill 350& \hfill 350\end{array}\right][/latex]
  14. Undefined; inner dimensions do not match.
  15. [latex]\left[\begin{array}{cc}\hfill 1,400& \hfill 700\\ \hfill -1,400& \hfill 700\end{array}\right][/latex]
  16. [latex]\left[\begin{array}{cc}\hfill 332,500& \hfill 927,500\\ \hfill -227,500& \hfill 87,500\end{array}\right][/latex]
  17. [latex]\left[\begin{array}{cc}\hfill 490,000& \hfill 0\\ \hfill 0& \hfill 490,000\end{array}\right][/latex]
  18. [latex]\left[\begin{array}{ccc}\hfill -2& \hfill 3& \hfill 4\\ \hfill -7& \hfill 9& \hfill -7\end{array}\right][/latex]
  19. [latex]\left[\begin{array}{ccc}\hfill -4& \hfill 29& \hfill 21\\ \hfill -27& \hfill -3& \hfill 1\end{array}\right][/latex]
  20. [latex]\left[\begin{array}{ccc}\hfill -3& \hfill -2& \hfill -2\\ \hfill -28& \hfill 59& \hfill 46\\ \hfill -4& \hfill 16& \hfill 7\end{array}\right][/latex]
  21. [latex]\left[\begin{array}{ccc}\hfill 1& \hfill -18& \hfill -9\\ \hfill -198& \hfill 505& \hfill 369\\ \hfill -72& \hfill 126& \hfill 91\end{array}\right][/latex]
  22. [latex]\left[\begin{array}{cc}\hfill 0& \hfill 1.6\\ \hfill 9& \hfill -1\end{array}\right][/latex]

Solving System of Equations using Matrices

  1. [latex]\left[\begin{array}{ccc}\hfill 0& \hfill 16& \hfill 4\\ \hfill 9& \hfill -1& \hfill 2\end{array}\right][/latex]
  2. [latex]\left[\begin{array}{ccc}\hfill 1& \hfill 5& \hfill 8\\ \hfill 12& \hfill 3& \hfill 0\\ \hfill 3& \hfill 4& \hfill 9\end{array}\right]\left[\begin{array}{c}\hfill 16\ \hfill 4\\ \hfill -7\end{array}\right][/latex]
  3. [latex]-2x + 5y = 5[/latex] [latex]6x-18y = 26[/latex] [latex]3x + 2y = 3[/latex]
  4. [latex]-x-9y + 4z = -1[/latex] [latex]8x + 5y + 7z = 8[/latex] [latex]4x + 5y-2z = 12[/latex]
  5. [latex]y + 58z = 2[/latex] [latex]8x + 7y-3z = -5[/latex]
  6. [latex](6, 7)[/latex]
  7. [latex](\dfrac{1}{5}, \dfrac{1}{2})[/latex]
  8. [latex](3, 4)[/latex]
  9. [latex](\dfrac{18}{13}, \dfrac{15}{13}, -\dfrac{15}{13})[/latex]
  10. [latex](x, -\dfrac{x}{2}, -1)[/latex]
  11. [latex](8, 1, -2)[/latex]
  12. [latex]860[/latex] red velvet, [latex]1,340[/latex] chocolate
  13. [latex]4%[/latex] for account 1, [latex]6%[/latex] for account 2
  14. [latex]$126[/latex]
  15. Banana was [latex]3%[/latex], pumpkin was [latex]7%[/latex], and rocky road was [latex]2%[/latex]
  16. [latex]100[/latex] almonds, [latex]200[/latex] cashews, [latex]600[/latex] pistachios

Solving Systems with Inverses

  1. [latex]AB = BA = \left[\begin{array}{cc}\hfill 1& \hfill 0\\ \hfill 0& \hfill 1\end{array}\right] = I[/latex]
  2. [latex]AB = BA = \left[\begin{array}{cc}\hfill 1& \hfill 0\\ \hfill 0& \hfill 1\end{array}\right] = I[/latex]
  3. [latex]AB = BA = \left[\begin{array}{ccc}\hfill 1& \hfill 0& \hfill 0\\ \hfill 0& \hfill 1& \hfill 0\\ \hfill 0& \hfill 0& \hfill 1\end{array}\right] = I[/latex]
  4. [latex]\dfrac{1}{29}\left[\begin{array}{cc}\hfill 9& \hfill 2\\ \hfill -1& \hfill 3\end{array}\right][/latex]
  5. [latex]\dfrac{1}{69}\left[\begin{array}{cc}\hfill -2& \hfill 7\\ \hfill 9& \hfill 3\end{array}\right][/latex]
  6. [latex]\dfrac{1}{17}\left[\begin{array}{ccc}\hfill -5& \hfill 5& \hfill -3\\ \hfill 20& \hfill -3& \hfill 12\\ \hfill 1& \hfill -1& \hfill 4\end{array}\right][/latex]
  7. [latex]\dfrac{1}{209}\left[\begin{array}{ccc}\hfill 47& \hfill -57& \hfill 69\\ \hfill 10& \hfill 19& \hfill -12\\ \hfill -24& \hfill 38& \hfill -13\end{array}\right][/latex]
  8. [latex]\left[\begin{array}{ccc}\hfill 18& \hfill 60& \hfill -168\\ \hfill -56& \hfill -140& \hfill 448\\ \hfill 40& \hfill 80& \hfill -280\end{array}\right][/latex]
  9. [latex](-5, 6)[/latex]
  10. [latex](2, 0)[/latex]
  11. [latex](\dfrac{1}{3}, -\dfrac{5}{2})[/latex]
  12. [latex](7, \dfrac{1}{2}, \dfrac{1}{5})[/latex]
  13. [latex](5, 0, -1)[/latex]
  14. [latex]\dfrac{1}{34}(-35, -97, -154)[/latex]
  15. [latex]\dfrac{1}{2}\left[\begin{array}{cccc}\hfill 2& \hfill 1& \hfill -1& \hfill -1\\ \hfill 0& \hfill 1& \hfill 1& \hfill -1\\ \hfill 0& \hfill -1& \hfill 1& \hfill 1\\ \hfill 0& \hfill 1& \hfill -1& \hfill 1\end{array}\right][/latex]
  16. [latex]\dfrac{1}{30}\left[\begin{array}{cccc}\hfill 3& \hfill 2& \hfill 1& \hfill -7\\ \hfill 18& \hfill -53& \hfill 32& \hfill 10\\ \hfill 24& \hfill -36& \hfill 21& \hfill 9\\ \hfill -9& \hfill 46& \hfill -16& \hfill -5\end{array}\right][/latex]
  17. [latex]\left[\begin{array}{cccccc}\hfill 1& \hfill 0& \hfill 0& \hfill 0& \hfill 0& \hfill 0\\ \hfill 0& \hfill 1& \hfill 0& \hfill 0& \hfill 0& \hfill 0\\ \hfill 0& \hfill 0& \hfill 1& \hfill 0& \hfill 0& \hfill 0\\ \hfill 0& \hfill 0& \hfill 0& \hfill 1& \hfill 0& \hfill 0\\ \hfill 0& \hfill 0& \hfill 0& \hfill 0& \hfill 1& \hfill 0\\ \hfill -1& \hfill -1& \hfill -1& \hfill -1& \hfill -1& \hfill 1\end{array}\right][/latex]
  18. [latex]50%[/latex] oranges, [latex]25%[/latex] bananas, [latex]20%[/latex] apples
  19. [latex]10[/latex] straw hats, [latex]50[/latex] beanies, [latex]40[/latex] cowboy hats
  20. Micah ate [latex]6[/latex], Joe ate [latex]3[/latex], and Albert ate [latex]3[/latex].
  21. [latex]124[/latex] oranges, [latex]10[/latex] lemons, [latex]8[/latex] pomegranates