Linear Algebra Answers

show that the set {(1,2,3),(0,1,2),(0,0,1) of vectors generates or span R^3

let v be the vector space of all ordered pair of real number check weather v is a vector space over t with respect to indicated operations if not state the axioms which fail to hold(a,b)+(c,d)=(a+b,c+d) K(a,b)=(K^2a,K^2b)

determine whether the vectors (1,3,-1,4),(3,8,-5,7),(2,9,4,23) in R^4 are linearly independent or linearly dependent 

what is homogeneous linear equation &nonhomogeneous linear equation?what is consistence&incossistence?

Prove that there does not exist a linear map T : R5->R5 such that

range T = null T.

Suppose S; T € L(V ) are such that ST = T S. Prove that null S is invariant under T.

Suppose V is finite-dimensional with dim V greater or equal to 2. Prove that

there exist S; T € L(V; V ) such that ST is not equal to T S.

Choose one type of matrix method (can be found in sections 6.2–6.6), describe the method, and give an example to illustrate how it might be used in a personal or professional scenario. In responding to your peers, comment on and ask questions about your classmates’ explanations of which method they would use for their particular application.

can you please help me I need to give an example on the matrix method and explain

Show that R 3 is a real vector space. Show that the set {(x, y, 0)|x, y ∈ R} is subspace of R 3 .

Solve by gaussian method

X+2Y-3Y=11

3X+2Y+Z=1

2X+Y-5Z=11