Summary
FSM - Matrices summary
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Full, in detail, summary of all matrices content needed for the final examination (Further Studies in Mathematics, Graph Theory and Matrices).
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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
. =
,
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