Let i = [-1 4] and j = [-4 1]. Find the following vectors. i = 62 i = -6j = | w = 62 – 6ỹ = = [ -

Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give D

Express the vector v =-1 as a linear combination of the vectors --3 V1 0,v2 4 and v3 -4 , if possible. Show all of the steps that you used %3D 3 -2 11 in obtaining your solution. 3.

Let →a=⟨−2,0,5⟩ and →b=⟨−3,−2,4⟩.Find the angle between the vectors (in degrees).

Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b = help (vectors)

1. Let x = i +4j + 2k and y = i-3j - k. In this question, write all vectors in i, j, k notation. (a) ( Find |x||. (b) M Find 2x + 3y. (c) Find x. y. (d) Find x × y. Answer: Answer: Answer:

Refer to the vectors below. b = [4, 3, 1] c = [1, -4, 1] d = [−1, −1, −3] Compute the indicated vector. 2b - 3c + d =

Evaluate the following vector expression: a = [3 -6 -2] -3 Calculate 3(ax + az) and enter your answer in the answer box below

Consider the vectors , v = , and w=. Simplify the expressions on the left column and match its value on the right column. u = zu + v 2v - w w + (u + v) W zu (v - w) - U :: :: :: :: :: :: :: ::

Find the sum and difference of the following vectors:     a. <-4,6>+<5,0> b. <-7,5>0<-5,-9>