Summary
FSM - Matrices summary
- Course
- Institution
Full, in detail, summary of all matrices content needed for the final examination (Further Studies in Mathematics, Graph Theory and Matrices).
[Show more]
Seller
Follow
ricciwaksman
Reviews received
Content preview
MATRICESDimensions rows columns b+3
leg , 2 x
4)
Elements Dualues in matrix
↳
=3rd row 1st
=
m row
amn As
n =
column
eg , column
major min Or
Major diagonal
[2I
taxx Ci . e . same rowt column
number
Minor
diagonal - other
diag
Identity matrix a
major diag= I's ;
rest=O's
Zerolnull matrix b all elements =
0 (Oman)
Upper triangle matrix/row echelon form elements below
major diag =o See
Lower
triangle matrix wall elements major diag above to
[ isI
Transpose =
Al= swap rows + columns (use to find inverse of 3+3)
Trace=tr(A)= for square matrices)
sum of
major diag (only .
Determinant =
det (A)
Inverse
-
A
=
Basic operations
+1 in the Same ( :. matrices must be same size)
add/subtract elements position
-
-
element is multiplied by the scalar
·
x
by Scalar every -> rows of one
I columns of other
must be same
matrix A has dimensions PXQ and matrix B has dimensions QxR
by
x - if matrix
answer matrix
B will have dimensions PXR
A multiplied by
row m of 1s matrix with column of 2nd matrix
->
for each position amn multiply
Find dimensions of answer (2 B
2x2 B 2)
(as] [
.
1 =
x x +
2 =
2x
-9. 2 Work out each
.
position
[ cy)
I
=(ap +
br +
(aq +
bx +
cz)
(dp+er+fy)(dq +
ex +
fz)
A B =
AXBY multiply by
=
: . inverse
Elementary row operations
You're allowed to a swap rows
-> multiply a row
by a scalar (non-zero)
multiple of one row to another
-> add the
Ri =
Re
3
Notation R, =
row 1 a
must use to annotate show what you doing e .
g R, FER ,
R new row I
↳ Ri
=
R - 2Rz
. =
,
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 ricciwaksman. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.43. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
79373 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now