Linear Algebra: Problems Based on Simultaneous Equations, Eigenvalues, Eigenvectors
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 nth power of a matrix A is the nth power of the eigenvalue of A 8. More properties: Sum of eigenvalues of a 2x2 matrix equals the sum of elements in the principal diagonal; product of eigenvalues equals the determinant 9. Computing the eigenvalues and eigenvectors 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 eigenvalue method to get a formula for the nth power of a matrix A. You might like to take a look at some of our other Linear Algebra tutorials :

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