Anadolu University, Environmental Engineering Department
NÜM 202 Linear Algebra and Numerical Methods
NÜM 202 LINEAR ALGEBRA AND NUMERICAL METHODS
(2015-2016 Academic Year, Fall Semester) HOMEWORK 1
1). Find the determinant of matrix A
1
0
𝐴=[
−5
−1
−4
4
−2
1
−4
2
−2
2
3
3
]
0
−4
2). Find the inverse of matrix A in Question1.
3). Solve the following system of equations using the inverse of the coefficient matrix.
-12x1 + x2 = -42
- 2x1 - 4x2 = -32
4). Solve the following system of equations using Gauss-Jordan elimination.
-2x1 + 4x2 – 2x3 + x4 = 1
-2x1 - 2x2 + 2x3 - 3x4 = -17
3x1 + 2x3 – 2x4 = -2
-4x1 + 2x2 + 3x3 + 2x4 = -13
5). Solve the system of equations in Question 4 using Gaussian Elimination with Backsubstitution.
6). Three matrices are given as below
𝐸= [
1 −2
]
3 0
4
𝐹=[
2
−1
]
6
0
𝐺=[
1
3
]
1
Show, using these matrices, that right distributivity holds for matrix multiplication
7). a) A sharpshooter makes 6 shots at a target. The shots are 4.57, 2.44, 4.55, 3.67, 4.29, 5.01 cm away from the
target. What is the accuracy of the shots? Report it with the correct number of significant digits.
b)We find the depth of a lake by two methods. Method A (Acoustic Measurement) is more accurate than Method
B (Sounding Line). Method A measures the depth as 14.62 meters and Method B as 15.41 meters. Calculate the
true error and the true percent relative error.
c) Round the numbers 4.6785 and 4.09 to 4 and 2 significant digits, respectively.
Due : October 26, 2015 (Bring to class in the first hour)
The answers will be posted at 12:00 at the website.
Homework format:
 Head page (Name of course, Homework No., Student name, number, Name of lecturer, Due date,
Signature)
 Questions and solution written by hand (readable and understandable, defining each step)
Your signature tells that you have completed this homework by your own effort.
Use only white A4 paper. Homeworks not following this format will not be accepted. Late homeworks will not
be accepted. Attach the papers together with a staple. Do not use pockets.
Prof. Dr. Erdem Ahmet Albek