18/3338–12FE Reference Handbook 10.4 · Mathematics · Linear Algebra

Handbook formula

2×2 Determinant and Inverse

Cramer’s rule and 2×2 inverses are the linear-algebra workhorses on FE Civil (force systems, best-fit, small stiffness). Invertible iff ad−bc ≠ 0.

Entries
Determinant

Step-by-step solved example

A=[[2,1],[0,4]]. Find det A and A inverse.

ABR
2×2 linear map sends basis vectors; det is the parallelogram area.
  1. 1. Determinant

    ad−bc=8−0=8.

  2. 2. Inverse

    (1/8)[[4,−1],[0,2]].

Answer: det=8; A^{-1}=(1/8)[[4,−1],[0,2]]

10 practice questions

0/10 correct

1.det[[3,1],[2,4]] =

2.A is singular when

3.Cramer’s x = det(Ax)/det(A) replaces

4.det(kA) for 2×2 equals

5.Inverse of [[1,0],[0,2]] is

6.det(AB)=

7.Trace of [[4,1],[2,3]] is

8.Solving Ax=b with A^{-1} is

9.det[[0,1],[1,0]] =

10.A 2×2 rotation matrix has det