Here you find exercises and solutions for Linear Algebra and related stuff.
Part 1 - Eigenvalues and Eigenvectors
In this video we consider a $2\times 2$ matrix, a $3\times 3$ matrix, and a $4\times 4$ matrix. In each case, we will calculate eigenvalue and eigenvectors.
Part 2 - Matrix Diagonalization
In this video we want to compute a power of a matrix, namely $A^{97}$. Doing the matrix multiplication so many times is not efficient at all. Therefore, we first diagonalize the matrix and calculate the power of the matrix decomposition.
Other videos related to this topic:
Part 3 - Solve System of Linear Equations
Let’s look at a system of linear equations. First we write it in the matrix notation with a right-hand side. Then we apply the Gaussian elimination to find the solution set.
Part 4 - Invert a Matrix
The inverse of a matrix can be calculated by solving the corresponding system of linear equations. However, for a $2 \times $-matrix, this is particularly easy and one gets a general formula for the inverse. Something you should remember for the future!
Part 5 - Matrix Equation
A linear matrix equation is just a combination of different systems of linear equations such that the Gaussian elimination also works there. However, since only a $2 \times 2$-matrix is involved, we can easily use the inverse of it to find the solution. We will demonstate the two solution methods.
Part 6 - Determinants
We know different methods for calculating the determinant of square matrices. Let’s practice them with different sizes of matrices.
Summary of the course Exercises - Linear Algebra
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