Summary
Samenvatting Lineaire Algebra
- Course
- Institution
Dit document bevat een samenvatting met voorbeelden van het vak Lineaire Algebra, behorende tot jaar 1 van de studie Farmaceutische Wetenschappen.
[Show more]
Seller
Follow
danielleband
Reviews received
Content preview
Samenvatting Lineaire AlgebraLengte van een vector: |(𝑎𝑏)| → √𝑎2 + 𝑏²
Scalar is een getal wat je met de vector vermenigvuldigd: 𝑐 (𝑎𝑏) = (𝑐𝑎
𝑐𝑏
)
Van a naar b = b – a
Van b naar a = a – b
Punt (a, b, c) → ai + bj + ck
Matrices vermenigvuldigen
𝑔 𝑗
(𝑑𝑎 𝑏 𝑐
𝑒 𝑓) ∙ (ℎ 𝑘 ) = (𝑚
𝑜
𝑛
𝑝)
𝑖 𝑙
2x3 3x2
m = ag + bh + ci
n = aj + bk + cl
o = dg + eh + fi
p = dj + ek + fl
Inverse
(10 0
1
= 𝐼2
)
1 0 0
(0 1 0) = 𝐼3
0 0 1
A ∙ I = 𝐴−1 → 𝐴−1 ∙ A = I
Ax = b → x = 𝐴−1 ∙ b
Getransponeerde matrix
𝐴𝑇 is de getransponeerde matrix. Dat wil zeggen 𝐴𝑗𝑖 → 𝐴𝑖𝑗 . Oftewel spiegelen in de hoofddiagonaal
1 4
A = (14 2 3
5 6
) 𝐴𝑇 = (2 5)
3 6
Een matrix heet symmetrisch als A = 𝐴𝑇
, Hoeken in een driehoek
𝑎2 = 𝑏 2 + 𝑐 2 - 2𝑏𝑐 cos 𝛼
𝑏 2 = 𝑎2 + 𝑐 2 - 2𝑎𝑐 cos 𝛽
𝑐 2 = 𝑏 2 + 𝑎2 - 2𝑏𝑎 cos 𝛾
In product
a∙b (𝑎𝑎1 ) ∙ (𝑏𝑏1 )
2 2
inproduct: 𝑎1 𝑏1 + 𝑎2 𝑏2
𝑎∙𝑏
Hoek tussen twee vectoren met behulp van in product: cos 𝛼 = |𝑎| |𝑏|
→ Er is een hoek van 90° als het inproduct 0 is.
Determinant
𝑎1 𝑏1
Determinant is → |𝑎 | = 𝑎1 𝑏2 − 𝑏1 𝑎2
2 𝑏2
𝑎 𝑑 𝑔 + − +
𝑒 ℎ 𝑑 𝑔 𝑑 𝑔
|𝑏 𝑒 ℎ| = a | |− + −|
𝑓 𝑖| – b | 𝑓 𝑖 | + c | 𝑓 𝑖 |
𝑐 𝑓 𝑖 + − +
Een matrix heeft een inverse als de determinant niet gelijk is aan 0
𝑎1 𝑏1 𝑥
(𝑎 ) ( ) = (𝑐𝑐1 ) → oplossen met de regel van Cramer
2 𝑏2 𝑦 2
𝑐1 𝑏1
|𝑐 |
2 𝑏2
→x= 𝑎1 𝑏1
|𝑎 |
2 𝑏2
𝑎1 𝑐1
|𝑎 𝑐2 |
→y= 𝑎1
2
𝑏1
|𝑎 |
2 𝑏2
Uitproduct
𝑎1 𝑏1 𝑐1
𝑎 𝑐
( 2 ) x (𝑏2 ) = ( 2 )
𝑎3 𝑏3 𝑐3
𝑖 𝑗 𝑘
𝑎
Oplossen van het uitproduct: | 1 𝑎2 𝑎3 |
𝑏1 𝑏2 𝑏3
𝑎2 𝑎3
→i = |𝑏 𝑏 |
2 3
𝑎1 𝑎3
→ j = |𝑏 𝑏 |
1 3
𝑎1 𝑎2
→ k = |𝑏 𝑏 |
1 2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller danielleband. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $6.03. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67866 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now