Linear Algebra Answers

Verify cayley hamiltan theorem for A=[ 124212421]

Given that k =[2 1]

[3 4]

Find the matrix k2+k+i,where i is the (2× 2) identify matrix

Find the dependency of vector (1,0,3),(0,1,2),(2,3,1),(4,1,0)

. Find a basis for the orthogonal complement of the vector v(1, 3,−2) of the euclidean vector space (R 3 , ·). Argue whether this basis is orthonormal or not.

Study whether the vectors v1(1, 1, 2), v2(2, 3, 0), v3(3, 4, 2) in R 3 are linearly dependent. If so, find the linear dependency relation

 Study whether the vectors v1(1, 1, 2), v2(2, 3, 0), v3(0, 1, 2) in R 3 are linearly independent.

Write v as a linear combination of u1, u2, u3, where

(a) v = (4, −9, 2), u1 = (1, 2, −1), u2 = (1, 4, 2), u3 = (1, −3, 2);

(b) v = (1, 3, 2), u1 = (1, 2, 1), u2 = (2, 6, 5), u3 = (1, 7, 8);

(c) v = (1, 4, 6), u1 = (1, 1, 2), u2 = (2, 3, 5), u3 = (3, 5, 8);

Find A if (A^-1-3I)^T= 2 [-1 2

5 4]

find the minimal polynomial of the linear operator t : R³ "- R³" define by t (x,y,z) =(x+2y+3z, 4y+5z,6 z).is t

find the inverse of the following matrix A and rank of a 2. 1. 2

1. 3. 0

-1. 1. 2