det(A)≠0
If det(A)≠0, A is invertible
Checklist subspace
contain zero vector,
closed under multiplication
closed under addition
Criteria for Basis
linearly independent, Span (V)
Inverse Matrix* Original Matrix
Row echolon
Rank of a matrix
Non- zero rows in echolon form
If Scalar Product of two matrices is 0
90° angle (orthogonal)
2x2 Determinante
1/ad-cb
Divergence test
if lim n->infinity an /= 0, then an will diverge
Integral test (f(x) is positive, continuous and decreasing in the interval
if integral is divergent -> f(x) is divergent
if integral is convergent -> f(x) is convergent
Domain of a function
Set of all inputs over which the function is defined
Range of a function
Set of all possible outputs
function is surjective if
range of (f) = y
d/dx (u*v)
udv/dx + v du/dx
Ratio test
lim -> infinity | an+1/an | = L if |L|<1, then series converges absolutely
Limit comparison test
if lim-> inf. an/bn is positive and finite, both converge or diverge