Question

Write true or false and give reason
The set{(x1.x2,...,xn)|x1,x2,...,xn∈R,x1=2x2+3} is a subspace of Rn. There is no 7×5 matrix of rank 6.
If V and V are vector spaces and T:V→V is a linear transformation,then whenever u1,u2,...,uk are linearly independent, Tu1, Tu2,...,Tuk are also linearly independent. If V is a vector space and T:V→V is a linear operator with det(T)=0,thenT is not diagonalisable.