LIN-01

2×2 determinant

Area of parallelogram.

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Lineardet 2

Governing equation

ad-bc

where

a: a (—)
b: b (—)
c: c (—)
d: d (—)
\det: det (—)

Lecture brief

Historical brief

Determinants, eigenvalues, least squares and Cayley–Hamilton are the nineteenth-century matrix craft behind every coupled system. The sheets invert, project and diagonalise small n. This sheet (LIN-01 — 2×2 determinant) is the form associated with det 2. Working symbols: $a$ , $b$ , $c$ , $d$ $\rightarrow$ $\det$ . Area of parallelogram.

Purpose

Purpose: compute

\det

from

a

b

c

d

in Linear algebra via

ad-bc

Area of parallelogram. Use it when a real linear algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

a = 3.000\,\mathrm{—}

b = 1.000\,\mathrm{—}

c = 2.000\,\mathrm{—}

d = 4.000\,\mathrm{—}

, the governing relation

ad-bc

yields

\det = 10.0000\,\mathrm{—}

. Area of parallelogram. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

a a3 —b b1 —c c2 —d d4 —

Outputs

det \det10.0000 —

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Narration of this film

Area of parallelogram.

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