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GATE ME 2021 Official Paper: Shift 1

Option 4 : Direction of p' = θ, ||p'|| = λ||p||

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__Concept: __

Eigen values and Eigen vector:

Is a linear transformation of a matrix A multiplied by a vector X to form:

AX = Y Where, Y is new vector.

AX = λX

Where λ = Eigen value, X → Eigen vector

The vector (λX) is in same direction of X but different in magnitude.

__Calculation: __

**Given: **

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**