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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) Solve the system of equations by Cramer’s rule (6 Marks) + 3 + 2 = 3 2 + 4 + 2 = 8 + 2 2 = 10 b) Let = 2 2 2 1 show that A is symmetric, reduce it to its diagonal form hence compute A10. (6 Marks) c) Reduce the matrix
=
4 1 6 1 2 5 6 3 4 to row echelon form. (6 Marks)
d) Let =
4 7 6 2 4 0 5 7 4 Find the minors and the cofactors of the elements in the first row hence compute . (6 Marks) e) Apply elimination method to solve + 2 + = 4 3 + 8 + 7 = 20 2 + 7 + 9 = 23 (6 Marks)
QUESTION TWO (20 MARKS)
a) Factorize the matrix A where
=
1 1 2 1 4 1 2 1 5 into the product of a lower and upper triangular matrix for which
2
i. The diagonal elements of the lower triangular matrix are 1. (4 Marks) ii. The diagonal elements of the upper triangular matrix are 1. (3 Marks) b) Find a lower triangular matrix L such that
= =
16 4 4 4 5 3 4 3 14

Hence find the solution of the set of equations 161 42 + 43 = 24 41 + 52 + 33 41 + 32 + 143 = 15 By Cholesky’s Method, find the determinant of L and A and show that the total number of multiplications needed to solve a system of n equations is 1 6 3 + 0(2). (13 Marks)
QUESTION THREE (20 MARKS)
a) Solve by Gauss Jordan elimination method the system by linear equations 2 + = 2 + 3 + 2 = 1 + + = 2 (8 Marks)
b) Let =
1 1 0 2 0 1 1 2 0

Find adjoint (A) hence compute A-1. (12 Marks)
QUESTION FOUR (20 MARKS)
a) Let =
1 3 2 2 2 1 1 4 3
Find; i. Tr (A) (2 Marks) ii. Rank (A). (6 Marks)
b) Let =
2 1 6 3 3 27 1 1 7
and let represent the eigen values of A. Form the
characteristics equation and obtain the Eigen values and eigen vectors of A. (12 Marks)

Ics2211:Numerical Linear Algebra Question Paper

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