Linear Algebra Answers

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If V is a vector space and T:V→V is a linear operator with det(T)=0,then T is not diagonalisable. The degree of the minimal polynomial of a 3×3 matrix is at most 2. viii) For any 2×2 matrix A,Adj(At)=(Adj(A))t. ix) x) The only matrix which is both symmetric and skew-symmetric is the zero matrix. There is no co-ordinate transformation that transforms the quadratic form x2+y2+z2 to the quadratic form xz+yz.

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.