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Summary Applied maths 214 A2 cheat sheet $3.66
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  2.  
  3. Stellenbosch University (SUN)
  4.  
  5. Applied mathematics 214 (AM214)

Summary

Summary Applied maths 214 A2 cheat sheet
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  • Course
  • Applied mathematics 214 (AM214)
  • Institution
  • Stellenbosch University (SUN)

This cheat sheet summary contains all the formulas and notes that are needed for the A2 exam of this module. The notes are brief but detailed where necessary to make it easy to see all the content as a whole.

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Document information

  • March 11, 2024
  • 15
  • 2023/2024
  • Summary

Subjects

  • applied maths

Written for

  • Stellenbosch University (SUN)
  • Applied mathematics 214 (AM214)
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Applied Maths Al Cheat Sheet (214)


Determinants
b
Properties
: a bec
: =




·
det (I) =
1

(AB) det (B) 3
booa
a
det (A) * :
·

det
=
.




if det(A) A
0 is
singular
·
=

,
" "
A -
LU
a b c
-9 . _


+
9 +
·

det/n) =

ode =
product of
diagonals

alefl-bl if cla
0 Of or +


dez
(Eij) (2) 1
00i
det
·
= =




·
det (A) =
det(LU) =
det (L) det (U) =
det (n)

permutations

Pizz (Pijk) I l
det
I a
row swap Ca
·
=
,




singularity
·
if A has zero row , det(A) =
0

·
If one row of A is a multiple of another now
,


det (A) =
0

A =
zU

det (A) =
detCU) =
0

·
dez (AP) =
det (A)
everything about rows
applies to col's


Al =
X

Eigenvalues ('stretch factors) only lengthens from pre-mult by A

if & is evec of A


tr(A) As I trace =
sum of diagonals)
=

Acc =
X
(A-XI) #
=
0 ( must be a basis for mull space of A-XI)
↳
only non-mull of if A-XI is
singular

, Want det/A-XI) =
0 (singual
-
characteristic
nth
degree polynomidh >
polynomial
-




of M
eigenvalues are roots



* -
tr (A) x + det(A) =
0
↓ ↓
Levals product evals




Eigenvectors : 2 Where (A-xI) = 0 Lie
.
Finding well space)
for each eval Xi ↳ use LU decomp
: UC =
0




Eigenvalue Decomposition

AlP =
X ,
24 , Al =
XuEz Acts =
XsEs
,




[Abs As Alpas I
,
=

[Xx , xx , xxc ]

I di itif i I
kai) e
A i



-
f


As =
S-
1
A S-S
-




=




Diagonal matrices 1
%08] =(i) "T
:




S"S-
"
A =




Eigenvalues Properties :


·
A is square
I A -XII
·
=
O

2x2 : = X- tr (A) + det (A) =
(X -




X(X -




B) =
x -


( + B)x + <B

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