G Problem 1. (4 points) Suppose A is a matrix of size 5 by 5. Which of the following statements must be TRUE? (I) Eigenvalue of A can be zero, but eigenvector of A cannot be a zero vector. (II) If λ is an eigenvalue of A, then the nullity of A − λI must be at least one. (III) If det(A − λI) = −(λ − 5)2 (λ + 4)3 then λ = 5 is said to have algebraic multiplicity 2 and λ = −4 is said to have algebraic multiplicity 3. (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III

-232

step-by-step explanation:

-4

step-by-step explanation:

do 6-10=

if u need it to be negative.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for