Ics2211:Numerical Linear Algebra Question Paper
Ics2211:Numerical Linear Algebra
Course:Business Information Technology
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
a) i) Show that if A and B are invertible square matrices of the same order, then AB is also invertible and 1 = 11. (6 Marks) ii) Using Gauss – Jordan method, find the inverse of the matrix
1 2 1 2 3 1 2 1 3 (5 Marks) b) i) Using Gauss elimination method find the solution of the following system of linear equations
1 2 + 3 = 4 21 + 2 33 = 0 1 + 2 + 3 = 2 (10 Marks)
ii) Find the Eigen values and Eigen vectors of the matrix.
= 3 1 1 1 3 1 3 3 1 (9 Marks)
QUESTION TWO (20 MARKS)
a) Prove that if the inverse of a square matrix exists, then it is unique. (5 Marks) b) Using the Partition method, find the solution of the linear system of equations below
2
1 + 2 + 3 = 1 41 + 32 3 = 6 31 + 52 + 33 = 4 (15 Marks)
QUESTION THREE (20 MARKS)
Given the matrix =
3 2 2 1 3 1 5 3 4
i. Find (3 Marks) ii. Find 1 (10 Marks) iii. Find the matrix B such that
=
3 4 2 1 6 1 5 6 4 (7 Marks)
QUESTION FOUR (20 MARKS)
Find the eigenpairs for the matrix
=
3 1 0 1 2 1 0 1 3
Also show that the eigenvectors are linearly independent. (20 Marks)
QUESTION FIVE (20 MARKS)
a) Given the system of linear equations + + = 6 + 2 + 3 = 10 + 2 + = Find the values of and for which the linear system has i. No solution (3 Marks) ii. A unique solution (3 Marks) iii. Infinite solution (4 Marks)
b) Find the solution to the linear system 21 + 32 3 = 4 1 22 + 3 = 6 1 122 + 53 = 10 By Cramer’s Rule. (10 Marks)
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