Linear Algebra Answers

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

Let U be the subspace of R5 denoted by U =  (x1; x2; x3; x4; x5) in R5 : x1 = 3x2 and x3 = 7x4 : (a) Find a basis of U. (b) Find a subspace W of R5 such that R5 = U "\\bigoplus" W.

show that any g€l(v, c) and u€v with g(u) not equal to 0 v=null g i{£u:£€c

let V={(a,b,c)€R³|a+b=c} and W={(a,b,c)€R³|a=b} be subspaces of R³.Is R³ direct sum of V and W?

If A = ( 1,2,3) (5,6,7) (0,1,4) and B = (1,0,3) ( 5,6,1) (2,1,4) then find i) AB ii) Inverse of A & B

suppose v are finite dimensional of t € l(v,w). show that with respect to each of bases of v and w, the matrix of t has at least dim range t nonzero entries

Assume that U is a plane. Find out whether or not the following vectors lie in U:

(10.1) ~u =< 3.8, 1 >, ~v =< −4, 1, 1 > and w~ = −~v

(10.2) ~u =< 3.8, 1 >, ~v =< −4, 1, 1 > and w~ = ~u − ~v

Example of Vector space and subspace in which it's all properties must satisfied.

2 Let A [ 1 𝑖 −𝑖 2 ] And let g be the form (on the space of 2x1 complex matrices) defined by g(X,Y) =Y*AX.Is g an inner product ?