Matrix Operations

CSC-212 · Semester III · Numerical Methods

Inverse of a 2×2 matrix

Guided practice — solve each problem, check, then generate a fresh one.

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Formula to apply

A⁻¹ = (1/det) [[d, −b], [−c, a]]

Problem

A⁻¹ has integer entries when det = ±1. Find A⁻¹ for A = [ 3 4 ] [ 2 3 ] Enter the four entries as top-left, top-right, bottom-left, bottom-right.

Working

  1. 1det = a·d − b·c = 3·3 − 4·(2) = 1.
  2. 2A⁻¹ = (1/1)·[ 3 -4 ; -2 3 ].
  3. 3Since det = 1: A⁻¹ = [ 3 -4 ; -2 3 ].