Search & Filtering
Find the determinant and inverse of:
a)
3 0
5 9
b)
−3 7 9
1 1 3
4 9 3
Check whether T(x1,x2,x3)=(x1+x2/x3,x3) define linear transformation from R3 to R2
determine whether or not the set of vectors {(1,2,-1),(0,3,1),(1,-5,3)} is a basis of R^3 also find dimension
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.
