Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Linear Algebra Inner Product Spaces, Orthonormal Basis
Let 〈., .〉 : ℝn × ℝn → ℝ be an inner product on the vector space ℝn over ℝ.
Consider the following statements:
P: |〈u, v〉| ≤ \(\frac{1}{2}\); (〈u, u〉 + 〈v, v〉) for all u, v ∈ ℝn.
Q: If 〈u, v〉 = 〈2u, -v〉 for all v ∈ ℝn, then u = 0.
Then
1
both P and Q are TRUE
2
P is TRUE and Q is FALSE
3
P is FALSE and Q is TRUE
4
both P and Q are FALSE