GATE 2023 PI – Question 49

Engineering Mathematics · Linear Algebra · 2 marks · Numerical answer

For $A=\begin{pmatrix}4&2\\3&3\end{pmatrix}$, find the eigenvalue associated with eigenvector $\begin{pmatrix}2\\-3\end{pmatrix}$ (integer).

Show answer and explanation

Correct answer: 1 to 1

Explanation

Multiplication gives $Av=(8-6,6-9)^T=(2,-3)^T=v$. Since Av = λv and v ≠ 0, **λ = 1**.

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