Mathematics II

• Chapter 1: Linear Equations in Linear Algebra. Notes and past questions on Linear Equations in Linear Algebra for TU BSc CSIT Mathematics II.
• Chapter 2: Transformation. Notes and past questions on Transformation for TU BSc CSIT Mathematics II.
• Chapter 3: Matrix Algebra. Notes and past questions on Matrix Algebra for TU BSc CSIT Mathematics II.
• Chapter 4: Determinants. Notes and past questions on Determinants for TU BSc CSIT Mathematics II.
• Chapter 5: Vector Spaces. Notes and past questions on Vector Spaces for TU BSc CSIT Mathematics II.
• Chapter 6: Vector Space Continued. Notes and past questions on Vector Space Continued for TU BSc CSIT Mathematics II.
• Chapter 7: Eigenvalues and Eigen Vectors. Notes and past questions on Eigenvalues and Eigen Vectors for TU BSc CSIT Mathematics II.
• Chapter 8: Orthogonality and Least Squares. Notes and past questions on Orthogonality and Least Squares for TU BSc CSIT Mathematics II.
• Chapter 9: Groups and Subgroups. Notes and past questions on Groups and Subgroups for TU BSc CSIT Mathematics II.
• Chapter 10: Rings and Fields. Notes and past questions on Rings and Fields for TU BSc CSIT Mathematics II.

• Define system of linear equations. When a system of equations is consistent? Make echelon form to solve: $-2a - 3b + 4c = 5$ $b - 2c = 4$... (2080)
• Define Linear Transformation with an Example Let $A = \begin{bmatrix} 1 & -3 \\ 3 & 5 \\ -1 & 7 \end{bmatrix}$, $v = \begin{bmatrix} -2 \... (2080)
• Find AB by block multiplication of the matrices. $$A = \begin{bmatrix} 2 & -3 & -1 & 0 & -4 \\ 1 & -5 & -2 & 3 & -1\\ 0 & -4 & -2 & 7 & -... (2080)
• Find the least square solution of $Ax = c$ where $$A = \begin{bmatrix} 1 & -3 & 3 \\ 1 & 5 & 1 \\ 1 & 7 & 2 \end{bmatrix}, \quad c = \beg... (2080)
• Determine the column of the matrix A are linearly independent where $A = \begin{bmatrix} 3 & -3 & 6 \\ 0 & 2 & 4 \\ 0 & 3 & 0 \end{bmatri... (2080)
• Let $A = \begin{bmatrix} 1 & 5 \\ -3 & 1 \end{bmatrix}$, $B = \begin{bmatrix} 4 & -5 \\ 3 & k \end{bmatrix}$ What value(s) of k, if any,... (2080)
• Evaluate the determinant of the matrix. $$\begin{bmatrix} 1 & -7 & 8 & 9 & -6 \\ 0 & 2 & -5 & 7 & 3 \\ 0 & 0 & 2 & 4 & -1 \\ 0 & 0 & 1 &... (2080)
• When two column vectors in $\mathbb{R}^2$ are equal? Give an example. Compute $u + 3v$, $u - 2v$, where $u = \begin{bmatrix} 1 \\ -3 \\ 2... (2080)
• Find the eigenvalue of $A = \begin{bmatrix} 7 & 3 \\ 3 & -1 \end{bmatrix}$ [5] (2080)
• Define null space of a matrix A. Let then show that v belongs to the null space matrix A. $A = \begin{bmatrix} 1 & -3 & 2 \\ -5 & 9 & -1... (2080)
• Find the equation $y = a_0 + a_1 x$ of the least squares line that best fits the data points (2,1), (5,2), (7,3), (8,3). [5] (2080)
• Show that the solutions of $y_{k+2} - 4y_{k+1} + 3y_k = 0$ are linearly independent. [5] (2080)
• Define group. Show that the set of integers is a group with respect to addition operation. [5] (2080)
• Define ring and show that set of positive integers with respect to addition and multiplication operation is not a ring. [5] (2080)
• Prove that the two vectors u and v are perpendicular to each other if and only if the line through u is perpendicular bisector of the lin... (2080)

Frequently asked questions

Based on the official syllabus.