Stuff

Question 1

det(A)≠0

Answer 1

If det(A)≠0, A is invertible

Question 2

Checklist subspace

Answer 2

contain zero vector,
closed under multiplication
closed under addition

Question 3

Criteria for Basis

Answer 3

linearly independent, Span (V)

Question 4

Inverse Matrix* Original Matrix

Answer 4

Row echolon

Question 5

Rank of a matrix

Answer 5

Non- zero rows in echolon form

Question 6

If Scalar Product of two matrices is 0

Answer 6

90° angle (orthogonal)

Question 7

2x2 Determinante

Answer 7

1/ad-cb

Question 8

Divergence test

Answer 8

if lim n->infinity an /= 0, then an will diverge

Question 9

Integral test (f(x) is positive, continuous and decreasing in the interval

Answer 9

if integral is divergent -> f(x) is divergent

if integral is convergent -> f(x) is convergent

Question 10

Domain of a function

Answer 10

Set of all inputs over which the function is defined

Question 11

Range of a function

Answer 11

Set of all possible outputs

Question 12

function is surjective if

Answer 12

range of (f) = y

Question 13

d/dx (u*v)

Answer 13

udv/dx + v du/dx

Question 14

Ratio test

Answer 14

lim -> infinity | an+1/an | = L if |L|<1, then series converges absolutely

Question 15

Limit comparison test

Answer 15

if lim-> inf. an/bn is positive and finite, both converge or diverge