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!
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: Let be a non singular matrix, 1+ p + p2+……..+ pn=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: N-th 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 (I-AB) is invertible, then (I-BA) is also invertible and (I-BA)-1 = I + B(I-AB)-1A
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