1 - Matrices Flashcards
matrix
an array of numbers
used to
- represent linear transformations
- solve linear simultaneous equations
dimensions of a matrix
its size
rows then columns
adding/ subtracting matrices
add together the corresponding elements of each matrix
square matrix
same no. rows and columns
zero matrix
all elements are zero
identity matrix I
ones in the leading diagonal
100
010
001
multiplying by I
AI = IA = A
multiplying matrices
star with the first row and column and sum the products of each pair - repeat for next column - then repeat for all the rows
- dimensions have to agree eg 2 2 x 23 = 2*3
raising to power
only square matrices
determinant of a 2*2
a b
c d
det(A) = ad - bc
if = 0 then its singular (no inverse)
if != 0 then its non-singular (has inverse)
inversing a 2*2
a b
c d
A-1 = 1/det(A) (d -b
-c a)
if Ax = y then A-1y = x
AA-1 = I
determinant of a 3*3
a b c
d e f
g h I
det(A) = a(det(efhi) + b(det(fdig) + c(det(degh)
minors matrix
for each element find the determinant of the 2*2 after the row and column with that element have been crossed out
transposing a matrix
where the rows and columns are interchanged (rows become columns columns become rows)
inversing a 3*3
- find det(A)
- find the minors matrix
- find matrix of co factors (+ - + etc)
- transpose
