Julia Pluto example.jl

Julia Pluto example.jl

### A Pluto.jl notebook ###
# v0.14.5

using Markdown
using InteractiveUtils

# ╔═╡ 0154ab9a-bf31-476c-a2f1-985d8cbf9508
using Plots

# ╔═╡ d2bddd28-1fff-48d5-8cb6-a59ad3275fda
using SymPy

# ╔═╡ 938e4cc1-55d3-4572-adb2-19ca57ddfb38
using LinearAlgebra

# ╔═╡ e5d4ac60-b383-11eb-196d-c1a8185270a0
M = [
	1 2
	3 4
]

# ╔═╡ 2d049c4f-42f7-4149-a921-114cb4f70ef9
z = [
	5
	6
]

# ╔═╡ f351df8a-6885-4f4b-9ded-c40474a0396a
M*z

# ╔═╡ 3f151a47-bbd5-449b-9d2a-b26a2db5bac7
f(x, y) = exp(-(x^2 + y^2)/2)

# ╔═╡ ec912f0c-536c-44b7-b4a3-de3ed063d3c2
let
	x = y = range(-3, 3; length=200)
	P1 = surface(x, y, f; colorbar=false)
	
	xs = ys = range(-3, 3; length=61)
	P2 = wireframe(xs, ys, f)
	
	P3 = heatmap(x, y, f)
	
	P4 = contourf(x, y, f)
	
	plot(P1, P2, P3, P4; size=(800, 600), layout=(2, 2))
end

# ╔═╡ 5c0f8a5f-9d8e-488d-b80f-bb733f200bff
a, b, c, d, p, q, r, s, λ = symbols("a b c d p q r s λ")

# ╔═╡ bc6783c2-775d-4b8c-acd5-2670a4ddcda6
A = [
	a b
	c d
]

# ╔═╡ 41a8f06f-a0d0-4b30-85ce-070e9798621b
B = [
	p q
	r s
]

# ╔═╡ f5e5bce5-d837-4c1c-84f9-2ad5a907f57e
C = A*B

# ╔═╡ 63472a6e-0ec0-4b41-8011-29ed3f14a1f0
det(C) |> factor

# ╔═╡ 338fd52b-dfc0-460f-90f6-e7671f22208f
det(A)*det(B)

# ╔═╡ 93f70b66-bd89-4fa3-acc6-17be92880d26
ϕ = det(λ*I - A)

# ╔═╡ a4c838a2-8a6c-4363-9a95-0dac750de132
solve(ϕ, [λ])

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