LIN-32

2×2 cofactor C11

(1,1) cofactor of 2×2.

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Governing2×2 cofactor C11

Governing equation

C_{11}=d

$d \in \left[-20, 20\right]$

where

d: d (—)
C: 2×2 cofactor C11 (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

C_{11}=d

$d \in \left[-20, 20\right]$

$d = -20$ $C = -20$

Along the curve

②

Domain of the variable — blue

d_{\min} = -20,\quad d_{\max} = 20

$d \in \left[-20, 20\right]$

$d = -20$ $d = -20$

Along the curve

③

Response curve — green

C_{11}=d

$d \in \left[-20, 20\right]$

$d = -20$ $C = -20$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}C}{\mathrm{d}d}

$d \in \left[-20, 20\right]$

$d = -19.75$ $C^{\prime} = 1$

Along the curve

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-32 — 2×2 cofactor C11) is the form associated with 2×2 cofactor C11. Working symbols: $d$ $\rightarrow$ $C$ . (1,1) cofactor of 2×2. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

C

from

d

in Linear algebra via

C_{11}=d

(1,1) cofactor of 2×2. 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

d = 4.000\,\mathrm{—}

, the governing relation

C_{11}=d

yields

C = 4.000\,\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

d d4 —

Outputs

2×2 cofactor C11 C4.000 —

Reading speed

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Narration of this film

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

(1,1) cofactor of 2×2. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube