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Summary Applied maths 214 A1 Cheat Sheet $3.32
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  2.  
  3. Stellenbosch University (SUN)
  4.  
  5. Applied mathematics 214 (AM214)

Summary

Summary Applied maths 214 A1 Cheat Sheet
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  • Course
  • Applied mathematics 214 (AM214)
  • Institution
  • Stellenbosch University (SUN)

This cheat sheet summarises the most important formulas and notes for applied maths 214 before the A1 assessment. They are brief but detailed where necessary to contain all that needs to be known for exams. Extra practice should be done and these notes should not be learnt in isolation for exams.

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Document information

  • March 11, 2024
  • 12
  • 2023/2024
  • Summary

Subjects

  • vectors

Written for

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

ors
, a e

(4)
q =
q = (a



product
D
& :
1 =
a , b, +
a b2 +
abs =
abcost a b = 0
torthogonal vectors

T
ba =
a b =
a xb axb =
0 >
-
norm to a adb



Norm
-




Hall = -
a a 9 2
+ +
=
a



a = * (a) = a (wit vector)




InR
-parameter
E =
p +
ta tz(- - 4),




Picto a *



↓
anchor
orientation
Vector
·. atto . . ,
(f ↓
T

1 =
p + ta

-
-




from
origin


in R
Pres cross product :
Normal
to plane

Pr es
through origin A =
Ax
parametric :




E =

q+ S& +
th =

2bs-a, bu) I
(a -

(a ,
b -A b
, , ,)f (a b2 -a b) T
,




Corthogonal)
Norm
1 .



1 =
0
vectors Acosrle
givenTe Angle
between


-bl
2
1) A =
a + b2-ZaBrosO
shift plane not
though origin
>
-




to position- replace I with -R
=> a tab +asby ,
= abos


Af
e ↓
e
scalar
=
] q .

b = abcost

, Matrics
- -
square matrices (nxn)

>
-

Matrix add is
LES :
·


(AT)" =
A
+
·
(A + B) =
At + BT
A+B =
B + A commutative
T

(B + C) (A + B) + (B) BA
·

A+ associative
=
= C
-




Face
>
-



scalar mult is :




↓A = AX commutative
-r(A) = a + A2 +
A33
-




>
-
Matrix melt is not commutative
(sum of diagonal)
of 2x2 :
Inverse

CABC=(ABILAme
e




(A + B) C
distributivig
=
AC + BL
Isame order At =ab [
1
(AT) (AT)
-




·
=




Permutation Matrix
>
-


Inverse matrix after row swapped metry
I
issameri, it stStab e
↳ swaps rows
pro-melt
>
-




Pt PT
I
=




i
Elementary row-op Matrix
e

Es ,
Marrie
Triangula
=




upper
:


-
matrices
Diagonal

I BoI (2008) Damon of = of t
L O
De D =
D"




premut by diagmai-scales theto
ens
-




-

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