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Lesson: Finding the Inverse of a Four-by-Four Matrix

Worksheet • 2 Questions

Q1:

Find 𝐴 βˆ’ 1 , given that

  • A ⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ βˆ’ 1 1 2 1 2 1 2 3 1 2 βˆ’ 1 2 βˆ’ 5 2 βˆ’ 1 0 0 1 βˆ’ 2 βˆ’ 3 4 1 4 9 4 ⎀ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ ⎦
  • B ⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ βˆ’ 1 1 2 1 2 1 2 3 1 2 βˆ’ 1 2 βˆ’ 5 2 βˆ’ 1 0 0 1 βˆ’ 2 βˆ’ 3 2 1 2 9 2 ⎀ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ ⎦
  • C ⎑ ⎒ ⎒ ⎣ βˆ’ 1 1 1 1 3 1 βˆ’ 1 βˆ’ 5 βˆ’ 1 0 0 1 βˆ’ 2 βˆ’ 3 1 9 ⎀ βŽ₯ βŽ₯ ⎦
  • D ⎑ ⎒ ⎒ ⎣ 1 0 0 0 0 1 βˆ’ 2 0 3 βˆ’ 1 3 βˆ’ 3 1 0 0 βˆ’ 1 ⎀ βŽ₯ βŽ₯ ⎦
  • E ⎑ ⎒ ⎒ ⎒ ⎒ ⎒ ⎒ ⎣ 0 0 1 0 1 0 βˆ’ 1 2 0 βˆ’ 1 3 1 βˆ’ 1 3 0 βˆ’ 8 9 βˆ’ 1 3 1 9 1 ⎀ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ βŽ₯ ⎦

Q2:

Using elementary row operations, find 𝐴 βˆ’ 1 , if possible, for the matrix

  • A 𝐴 = 1 4 ⎑ ⎒ ⎒ ⎣ 3 βˆ’ 2 1 βˆ’ 5 βˆ’ 2 1 6 βˆ’ 6 2 0 βˆ’ 8 4 0 1 βˆ’ 2 βˆ’ 1 1 ⎀ βŽ₯ βŽ₯ ⎦ βˆ’ 1
  • B The matrix has no inverse.
  • C 𝐴 = ⎑ ⎒ ⎒ ⎣ βˆ’ 2 5 βˆ’ 2 3 3 βˆ’ 2 1 βˆ’ 5 0 βˆ’ 2 1 0 1 βˆ’ 1 0 βˆ’ 1 ⎀ βŽ₯ βŽ₯ ⎦ βˆ’ 1
  • D 𝐴 = ⎑ ⎒ ⎒ ⎣ 3 βˆ’ 2 1 βˆ’ 5 βˆ’ 2 5 βˆ’ 2 3 0 βˆ’ 2 1 0 βˆ’ 1 1 0 1 ⎀ βŽ₯ βŽ₯ ⎦ βˆ’ 1
  • E 𝐴 = 1 4 ⎑ ⎒ ⎒ ⎣ 3 βˆ’ 2 1 βˆ’ 5 βˆ’ 2 5 βˆ’ 2 3 0 2 βˆ’ 1 0 1 βˆ’ 1 0 βˆ’ 1 ⎀ βŽ₯ βŽ₯ ⎦ βˆ’ 1
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