Question
Consider a vector p in 2-dimensional space. Let its direction (counter-clockwise angle with the positive x -axis) be θ . Let p be an Eigen vector of a 2 ×2 matrix A with corresponding Eigen value λ , λ > 0 . If we denote the magnitude of a vector ν by ν , identify VALID statement regarding p ' , where p ' = Ap
Options :
Direction of 𝑝′ = 𝜆𝜃, ‖𝑝′‖ = ‖𝑝‖
Direction of 𝑝′ = 𝜃, ‖𝑝′‖ = 𝜆‖𝑝‖
Direction of 𝑝′ = 𝜆𝜃, ‖𝑝′‖ = 𝜆‖𝑝‖
Direction of 𝑝′ = 𝜃, ‖𝑝′‖ = ‖𝑝‖/𝜆
Answer :
Direction of 𝑝′ = 𝜃, ‖𝑝′‖ = ‖𝑝‖/𝜆
Solution :
A is 2 × 2 matrix and p is Eigen vector of matrix A with Eigen value λ
p’ = Ap
By definition of Eigen vector & values :
Ap = λp
p’ = λp
||p’|| = ||λp||
||p’|| = λ||p||
Direction of vector p’ will be same as vector p = θ
Copyright © 2025 Test Academy All Rights Reserved