Linear Algebra Answers

 Let W be the set of all vectors o the form

[ 5b + 2c

b

c ] where b and c are arbitrary. Find vectors u and v such that W = span{u, v}.

Let u=(-1/2,-1,2/3) ,v=(4,-1,-3) and θ=1/2. Find

i) u.θv

ii)A non-zero vector orthogonal to both u and v

Question1

 

Given   matrix A =        2      2     1
                          1      3     1
                          1      2     2

 
 

1.1 find the eigenvalues of   A

 
1.2.   Determine an eigenvector for the eigenvalue  =  5

Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, −4,0), v = (−1, −1,2,2),

and w = (3,2,5,4).

A is a 2x2 matrix

Let A = {(2) (0) (0) (-1)}. Find A³²

Write the polynomial x^2+4x-3 as a linear combination of 2x^2-3x and x^2-2x+5 and x+3