LIN-30

Singular 2×2 test

Vanishes iff columns are dependent.

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GoverningSingular 2×2 test

Governing equation

\\det=ad-bc

where

a: a (—)
b: b (—)
c: c (—)
d: d (—)
det: Singular 2×2 test (—)

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-30 — Singular 2×2 test) is the form associated with Singular 2×2 test. Working symbols: $a$ , $b$ , $c$ , $d$ $\rightarrow$ $det$ . Vanishes iff columns are dependent. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

det

from

a

b

c

d

in Linear algebra via

\\det=ad-bc

Vanishes iff columns are dependent. 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 = 1.000\,\mathrm{—}

b = 2.000\,\mathrm{—}

c = 2.000\,\mathrm{—}

d = 4.000\,\mathrm{—}

, the governing relation

\\det=ad-bc

yields

det = 0.000\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

a a1 —b b2 —c c2 —d d4 —

Outputs

Singular 2×2 test det0.000 —

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Vanishes iff columns are dependent. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube