VTU | 1st Sem |Maths Module 3 2025 Scheme| Eigenvalues and Eigenvectors | Matrix Problem | 1BMATS101

Welcome to Express VTU 4 All, your reliable YouTube channel for VTU 1st Semester Mathematics (1BMATS101) explained step by step according to the VTU 2025 Scheme.
In this video, we solve an important problem from Module 3 – Eigenvalues and Eigenvectors, where we are asked to find the eigenvalues and corresponding eigenvectors of a given square matrix.
This is a very frequently asked VTU examination question (2025 Scheme) and carries high weightage, especially in linear algebra and matrix topics.
🔹 Question
Determine the eigenvalues and corresponding eigenvectors for the matrix
[ 8 -6 2
-6 7 -4
2 -4 3 ]
🔹 Concepts Covered in This Video
✔ Eigenvalues of a matrix
✔ Eigenvectors
✔ Characteristic equation
✔ Determinant of a matrix
✔ Solving |A − λI| = 0
✔ Finding eigenvectors for each eigenvalue
✔ VTU exam-oriented approach (2025 Scheme)
🔹 Method Explained (Step-by-Step)
In this video, we follow these steps:
1️⃣ Form the characteristic equation |A − λI| = 0
2️⃣ Expand the determinant
3️⃣ Solve the characteristic equation to find eigenvalues
4️⃣ Substitute each eigenvalue into (A − λI)x = 0
5️⃣ Solve the system to find eigenvectors
6️⃣ Write eigenvectors corresponding to each eigenvalue clearly
Each step is explained neatly in VTU answer-writing format so that students can easily reproduce it in exams.
🔹 Why This Question Is Important (2025 Scheme)
✔ Direct question from Module 3 syllabus
✔ Very common VTU PYQ
✔ Important for understanding diagonalization of matrices
✔ Foundation for engineering applications
✔ Easy full marks if steps are written properly
💡 VTU Exam Tips (2025 Scheme)
✅ Always write the characteristic equation clearly
✅ Show determinant expansion steps
✅ Write eigenvalues separately
✅ Find eigenvectors for each eigenvalue
✅ Final answers must be clearly boxed

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