Engineering Mathematics-I Unit 1 – Matrices: AKTU previous year questions
12 AKTU questions from Unit 1 (Matrices) asked in 2024–2026, tagged by marks, year and topic. In short: about 28 marks of every paper come from this unit; the most asked topic is Eigenvalues and Eigenvectors (11 times); 6 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
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)
- 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)
- 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)
- Find two non-singular matrices P and Q such that PAQ is in normal form, Where $A = \begin{bmatrix} 1 & 3 & 6 & -1 \\ 1 & 4 & 5 & 1 \\ 1 & 5 & 4 & 3 \end{bmatrix}$. (7 marks, 2025, Elementary Transformations)
- 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)
- Discuss for all values of K for the system of equations $x + y + 4z = 6, x + 2y - 2z = 6, Kx + y + z = 6$ as regards existence and nature of solution. (7 marks, 2025, Solution of Systems of Linear Equations)
- Find the product and sum of the eigen values for $A=\begin{bmatrix}8&-4\\2&2\end{bmatrix}$. (2 marks, 2024, Eigenvalues and Eigenvectors)
- Solve the system of homogenous equations: $ x_1+x_2+x_3+x_4=0,\quad x_1+3x_2+2x_3+4x_4=0,\quad 2x_1+x_3-x_4=0. $ (7 marks, 2024, Solution of Systems of Linear Equations)
- 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)
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
Unit 1 question pattern
- 2-mark questions: 4 asked in 2024–2026
- 7-mark questions: 8 asked in 2024–2026
- About 28 marks from Unit 1 in every paper
- 6 questions were asked again in a later year
Unit 1 questions year by year
- 2026: 5 Unit 1 questions asked (25 marks across that year's papers)
- 2025: 4 Unit 1 questions asked (23 marks across that year's papers)
- 2024: 3 Unit 1 questions asked (16 marks across that year's papers)