Simultaneous equations by matrices — A/L Combined Mathematics

How do I practise Simultaneous equations by matrices?

1 question with a worked solution

Check before you answer: Matrix Equation Formulation: Correctly writing the given equations as AX = B, showing all matrix components clearly.

1. Using matrix inversion to solve the simultaneous system: 2x + y = 7 and 5x + 3y = 19, what is the solution vector [x, y]ᵀ?
   1. A) x = 2, y = 3
   2. B) x = 1, y = 5
   3. C) x = 3, y = 1
   4. D) x = 4, y = -1
   Check my answer

   Correct answer: A) x = 2, y = 3

   System is A X = B with A = [[2, 1], [5, 3]], X = [x, y]ᵀ, B = [7, 19]ᵀ. As det(A) = 6 - 5 = 1, A⁻¹ = [[3, -1], [-5, 2]]. Then X = A⁻¹ B = [[3, -1], [-5, 2]] [7, 19]ᵀ = [3(7) - 1(19), -5(7) + 2(19)]ᵀ = [21 - 19, -35 + 38]ᵀ = [2, 3]ᵀ. Thus, x = 2 and y = 3.

   Show worked solution

   Step 1: X = A⁻¹ B = [[3, -1], [-5, 2]] · [7, 19]ᵀ. Step 2: x = 3(7) - 19 = 2; y = -5(7) + 2(19) = 3. Answer: x = 2, y = 3.
   Modelled on: the A/L Combined Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Simultaneous equations by matrices fit in the syllabus?

Year 2 · Term 1