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 IITJEE, Anyone else who needs this Tutorial as a reference!Linear Algebra  Matrices Part II  Outline of Contents:
In this tutorial, we introduce a few solved problems to help you understand the concepts introduced in PartI. 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: Let be a non singular matrix, 1+ p + p^{2}+……..+ p^{n}=0 (0 denotes the null matrix) then p^{1}= ... ? Q: Finding the characteristic equation of a given matrix Q: When does the inverse of a diagonal matrix exist (if at all) ? Q: A trust fund had Rs. 50000 that is to be invested into two types of bonds. The first bond pays 5% simple interest per year and the second bond pays 6% simple interest per year.Using matrix multiplication determine how to divide Rs. 50000 among the two types of bonds so as to obtain an annual total interest of Rs.2780. Q: Computing the inverse of a given matrix using elementary row transformations or otherwise. Q: Finding the rank of a given matrix. 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: Nth power of a matrix Q: Systems of recurrence relations Q: Rank of a matrix Q: Let A and B be matrices of order n. Prove that if (IAB) is invertible, then (IBA) is also invertible and (IBA)^{1} = I + B(IAB)^{1}A 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 Tutorial with Solved Problems :You might like to take a look at some of our other Linear Algebra tutorials :

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