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## Our Linear Algebra Tutorials: at a glanceLinear Algebra - Matrices Part I - A Tutorial with ExamplesLinear Algerba - Matrices Part II - Tutorial with Problems and SolutionsLinear Algebra - Determinants - A Tutorial with Problems and SolutionsLinear Algebra - Simultaneous Equations in Multiple Variables Basic Concepts In Linear Algebra and Vector Spaces - A Tutorial with Examples and Solved ProblemsLinear Algebra - Introductory Problems Related to Vector SpacesLinear Algebra - More about Vector SpacesLinear Algebra - Linear Transformations, Operators and MapsLinear Algebra - Eigenvalues, Eigenvector,Cayley Hamilton TheoremLinear Algebra - Problems on Simultaneous Equations, EigenvectorsLinear Algebra - A few closing problems in Recurrence Relations

Linear Algebra: Problems Based on Simultaneous Equations, Eigenvalues, Eigenvectors
 Demonstrating the Crammer rule, using eigenvalue methods to solve vector space problems, verifying Cayley Hamilton Theorem, advanced problems related to systems of equations. Solving a system of differential equations .

1. Solving a system of linear equations using augmented matrix method and using echelon forms.
2. Finding the condition for a system of linear equations to be consistent.
3. Testing a system of linear equations for consistency.
4. Applying Cramer's rule
5. Handling a system which does not have a unique solution.
6. Finding the characteristic equation of a matrix.
7. Proving properties related to eigenvalues: such as, the eigenvalue of the n-th power of a matrix A is the n-th power of the eigen-value of A
8. More properties: Sum of eigen-values of a 2x2 matrix equals the sum of elements in the principal diagonal; product of eigen-values equals the determinant
9. Computing the eigen-values and eigen-vectors of 2x2 and 3x3 matrices.
10. Checking for the conditions when a
homogeneous system have
a non–trivial solution.
11. Verifying Caley Hamilton theorem for a matrix; finding inverse of a matrix.
12. Using the eigen-value method to get a formula for the n-th power of a matrix A.