Answer to Question #327898 in Linear Algebra for Dudu

Question

1.find a number T such that (3,1,4),(2,-3,5),(5,9,t) is not linearly independent in R³.

2.let v be the subspace of R⁵ defined by v={(x1,x2,x3,x4, X5)€R⁵:2x1=x2 and X3=X5}

2.1.find a basis of v.

2.2.find a subspace w of R⁵ such that R⁵=v©w.

3.suppose v1,v2,...VM are finite-dimensional subspace of v.prove that v1+v2+...+VM is finite-dimensional and dim(v1+v2+....+VM)is greater or equal dimv1+dimv2+...+dimvm.