Linear Algebra Answers

Question. Given the matrix A = 3 1 1

2 4 2

1 1 3

a. Solve A for its eigen values and given vectors

b. Constant Similar matrix for A if possible

Question 1. Let u = (2,1,0,5) e R². Apply the process of inner product spaces.

• Solve u for its length
• Solve u for its Normalized vector

Let T

 be a function from R

3

→R

3

 defined by

T(x,y,z)=(x−y+2z,2x+y,−x−2y+2z)

(i)

(ii)

  Show that T is a Linear Transformation

  Find nullity of T

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