LIN-23

Cramer x

2×2 Cramer x.

Reading speed

GoverningCramer x

Governing equation

x=\\det(A_x)/\\det A

where

a: a (—)
b: b (—)
c: c (—)
d: d (—)
e: e (—)
f: f (—)
x: Cramer x (—)

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-23 — Cramer x) is the form associated with Cramer x. Working symbols: $a$ , $b$ , $c$ , $d$ , $e$ , $f$ $\rightarrow$ $x$ . 2×2 Cramer x. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

x

from

a

b

c

d

e

f

in Linear algebra via

x=\\det(A_x)/\\det A

2×2 Cramer x. 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 = 2.000\,\mathrm{—}

b = 1.000\,\mathrm{—}

c = 1.000\,\mathrm{—}

d = -1.000\,\mathrm{—}

e = 5.000\,\mathrm{—}

f = 1.000\,\mathrm{—}

, the governing relation

x=\\det(A_x)/\\det A

yields

x = -6.000e+9\,\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 a2 —b b1 —c c1 —d d-1 —e e5 —f f1 —

Outputs

Cramer x x-6000000000.000 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

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

2×2 Cramer x. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube