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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                                                                                                                                                           ------------xxxx------------

Linear Algebra: Matrices Part II

#### Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE, Anyone else who needs this Tutorial as a reference!

 Problems and solved examples based on the sub-topics mentioned above. Some of the problems in this part demonstrate finding the rank, inverse or characteristic equations of matrices. Representing real life problems in matrix form.

In this tutorial, we introduce a few solved problems to help you understand the concepts introduced in Part-I.

Here are some quick notes on the kind of problems explained in this tutorial :

Q: In an upper triangular matrix n×n, minimum number of zeros is ... ?

Q: 2n-1

Q:

Q:

Q:

Q:

Q:

Q: Finding the circumstances under which a matrix will be invertible.

Q: Under what conditions does the inverse of a diagonal exist?

Q: Find all the matrix which commute with a given matrix.

Q: Compute the inverse of a matrix.

Q: Using elementary row transformations find the inverse of the matrix.

Q: N-th power of a matrix

Q: Systems of recurrence relations

Q: Rank of a matrix

Q: is also invertible and (I-BA)-1-1

References:

1. Linear Algebra by Kenneth Hoffman and Ray Kunze

2. Linear Algebra by K. R. Matthews, University Of Queensland

3. Mathematics by Amit M Agarwal

4. Mathematics by M.L Khanna