Here is a collection of Lay Problems in Linear Algebra. These problems are designed to help you understand the concepts and applications of linear algebra.
Introduction
Linear algebra is a branch of mathematics that deals with linear equations, linear transformations, and vector spaces. It has wide applications in various fields such as physics, engineering, computer science, and economics.
Problem Set
Matrix Representation
Find the matrix representation of the linear transformation ( T ) that rotates a point in the plane by 90 degrees counterclockwise.Eigenvalues and Eigenvectors
For the matrix (\begin{bmatrix} 4 & 2 \ 2 & 1 \end{bmatrix}), find the eigenvalues and eigenvectors.Solving Systems of Linear Equations
Solve the following system of linear equations:
[ \begin{cases} 2x + 3y = 8 \ x - y = 1 \end{cases} ]Determinants
Calculate the determinant of the matrix (\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}).Change of Basis
Find the change of basis matrix from the standard basis to the basis ({(1, 2), (3, 4)}).
For more exercises and resources on linear algebra, check out our Linear Algebra Tutorial.