Engineering Mathematics-I Unit 1 – Matrices: important questions for AKTU
Unit 1 (Matrices) questions that AKTU repeats most often. This unit carries about 28 marks per paper. Start with the repeated questions, then the most asked topics.
Most repeated Unit 1 questions
- Find the eigen values and eigen vectors of the following Matrix A: $A = \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix}$. (7 marks, 2026, Eigenvalues and Eigenvectors) – also asked in 2021, 2022, 2023, 2024, 2025
- Find the eigen values and eigen vectors of the following matrices: $A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix}$. (7 marks, 2025, Eigenvalues and Eigenvectors) – also asked in 2021, 2022, 2023, 2024, 2026
- Determine eigen vectors for the matrix $A=\begin{bmatrix}1&2&2\\0&2&1\\-1&2&2\end{bmatrix}$. (7 marks, 2024, Eigenvalues and Eigenvectors) – also asked in 2021, 2022, 2023, 2025, 2026
Most important Unit 1 topic
- Eigenvalues and Eigenvectors (Unit 1: Matrices) – asked 11 times in 2019, 2021, 2022, 2023, 2024, 2025, 2026
Most asked Unit 1 topics
- Eigenvalues and Eigenvectors – asked 11 times
- Rank of a Matrix – asked 7 times
- Solution of Systems of Linear Equations – asked 7 times
More Unit 1 previous year questions
- In the matrix equation $\begin{bmatrix} 3 & -1 \\ 2 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ -3 \end{bmatrix}$, what are the values of x and y? (2 marks, 2026, Solution of Systems of Linear Equations)
- Find the Rank of the following Matrix A: $A = \begin{bmatrix} 2 & -4 & 6 \\ -1 & 2 & -3 \\ 3 & -6 & 9 \end{bmatrix}$. (2 marks, 2026, Rank of a Matrix)
- Determine the values of $\lambda$ and $\mu$ such that the system $2x-5y+2z=8$, $2x+4y+6z=5$, $x+2y+\lambda z=\mu$ has (i) no solution, (ii) a unique solution, and (iii) infinitely many solutions. (7 marks, 2026, Solution of Systems of Linear Equations)
- If $X_1 = \begin{bmatrix} 3 \\ 1 \\ -4 \end{bmatrix}, X_2 = \begin{bmatrix} 2 \\ 2 \\ -3 \end{bmatrix}, X_3 = \begin{bmatrix} 0 \\ -4 \\ 1 \end{bmatrix}$, then show that the vectors $X_1, X_2, X_3$ are linearly dependent. (7 marks, 2026, Linear Dependence and Independence of Vectors)
- Find the eigen values of the matrix $\begin{bmatrix} \cos\theta & -\sin\theta \\ -\sin\theta & -\cos\theta \end{bmatrix}$. (2 marks, 2025, Eigenvalues and Eigenvectors)
Unit 1 syllabus topics
- Elementary Transformations
- Inverse of a Matrix
- Rank of a Matrix
- Solution of Systems of Linear Equations
- Characteristic Equation
- Cayley-Hamilton Theorem and Its Applications
- Linear Dependence and Independence of Vectors
- Eigenvalues and Eigenvectors
- Complex Matrices: Hermitian, Skew-Hermitian and Unitary
- Applications of Matrices to Engineering Problems