answer d only. Prove (by giving a proof) or disprove (by giving a counterexample)each of the following statements. (Note : You will not get any credit if youanswer only True or False.)(a) Let V and W be finite dimensional vector spaces, and T : V → W be alinear transformation. If T is one-to-one then dim V < dim W.(b) For all linear operators T : V → V, imT is a T-invariant subspace of V.(c) If A, B arenxn positive definite symmetric matrices, then for any scalarsa, b > 0, aA+ bB is also positive definite.(d) If S, T are symmetric linear operators on an inner product space V, thentheir composition ST is also symmetric.

Name: answer d only. Prove (by giving a proof) or disprove (by giving a coun
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: answer d only. Prove (by giving a proof) or disprove (by giving a counterexample)each of the following statements. (Note : You will not get any credit if youanswer only True or False.)(a) Let V and W be finite dimensional vector spaces, and T : V → W