Transpose and inverse of a matrix — A/L Combined Mathematics

How do I practise Transpose and inverse of a matrix?

1 question with a worked solution

Check before you answer: Product Reversal Law Application: Applying (AB)^T = B^T A^T and (AB)⁻¹ = B⁻¹ A⁻¹ in theoretical matrix proofs.

1. What is the inverse matrix A⁻¹ of the 2 × 2 invertible matrix A = [[2, 1], [5, 3]]?
   1. A) [[2, -1], [-5, 3]]
   2. B) [[3, 1], [5, 2]]
   3. C) [[3, -1], [-5, 2]]
   4. D) [[-3, 1], [5, -2]]
   Check my answer

   Correct answer: C) [[3, -1], [-5, 2]]

   Determinant det(A) = ad - bc = (2)(3) - (1)(5) = 6 - 5 = 1. The inverse of [[a, b], [c, d]] is (1/det(A)) [[d, -b], [-c, a]]. Substituting gives (1/1) [[3, -1], [-5, 2]] = [[3, -1], [-5, 2]].

   Show worked solution

   Step 1: det(A) = 2(3) - 1(5) = 1. Step 2: A⁻¹ = (1/1) · [[3, -1], [-5, 2]] = [[3, -1], [-5, 2]]. Answer: [[3, -1], [-5, 2]].
   Modelled on: the A/L Combined Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Transpose and inverse of a matrix fit in the syllabus?

Year 2 · Term 1