Q Flashcards
(17 cards)
Parametric eq parallel through points?
direction vectors are those
Directional derivative relation to direction vector (if in the direction of direction vector)?
direction derivative at direction vector terms except p.d at the point (a,b,…) is the slope of d
where slope of d = d4/ mag d1,d2,d3
zero function?
f(X) +z(x) = f(x)
Lin span of x?
the set of all linear combinations of the vectors in X
At b->b x (f1)b ?
whatever eigenvalue x (f1)b
as At b->b x (f1)b = A(f1) u just put in terms of basis
det (A) in PDP^-1 what does it tell us?
the eigenvalues multiplied equals the det of symmetric matrix
CS(A)=?
Lin (X)
Parametric eq for a linear transformation Ax=…?
Null space parameters + particular vector which is given or you calc
Rank of T?
dimension of the range of T
Nullity of T?
dimension of the kernel of T
Rank nullity theorem of T?
Rank (T) +Nullity (T) = dim (V)
Conclusive principle minors?
if det does not equal 0
Saddle point principle minors?
for a 3x3 matrix if second principle minor = 0
Direction vector relation to normal?
orthogonal
Vertical plane for cart what is excluded?
LHs=0
Horizontal plane what is excluded?
gradient = 0 , so just z terms (contour)
Show linear transformation effectively?
Prove T(f⊕g) = T(f) ⊕ T(g)
and T(λ⊙f)=λ⊙T(f)
