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MATLAB Homework 2

This homework assignment involves vector and matrix operations in MATLAB. Students are asked to normalize vectors in various ways, find the determinant and inverse of matrices, extract columns and rows of matrices to form new matrices, and extract submatrices from a given matrix. The submission must include MATLAB code and corresponding output.

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124 views2 pages

MATLAB Homework 2

This homework assignment involves vector and matrix operations in MATLAB. Students are asked to normalize vectors in various ways, find the determinant and inverse of matrices, extract columns and rows of matrices to form new matrices, and extract submatrices from a given matrix. The submission must include MATLAB code and corresponding output.

Uploaded by

smith
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Introduction to Wireless Communication (EE 4365)

MATLAB Homework 2

Due: Tuesday 9/07/2022 (11:59 PM)

• This homework is a continuation of vector and matrix operations in MATLAB.

• The names of the functions you’ll need to look up are provided in bold where
needed.

• Your submission will include the MATLAB code followed by its corresponding
outputs in a .txt file (or a MATLAB script file).

Problem 1: Vector Normalization

(a) Create a vector x = ei2t/3 , where t = [1, 2, ..., 10]. Find the norm of vector x,
which can be denoted as |x| (DO NOT use norm).

(b) Magnitude normalization: Normalize the vector x such that |x| = 1 (use norm).

(c) Zero-mean normalization: Normalize the vector x such that it has a mean of 0
(use mean).

(d) Minmax normalization: Normalize the vector t so all of its values are between
0 and 1 (use min and max).

(e) Normalize the vector x such that it has a mean of -5 (use mean).

Problem 2: Matrix Inverse and determinant


 
1 1 1
(a) Create a square matrix A = 2 2 2 and find |A|.
3 3 3

(b) Is the matrix A invertible? If not, why?


 
1 0 0
(c) Create a square matrix B = 1 1 0 and find |B|.
0 1 1

(d) Is the matrix B invertible? If yes, find B−1 .

1
2

Problem 3: Vector Extraction


 
1 1 0
(a) Create a square matrix A = 0 1 1. Extract the columns of matrix A as
1 0 1
column vectors c1 , c2 , c3 and the rows as row vectors r1 , r2 , r3 . (c1 is the first
column of A, r1 is the first row of A and so on)
 T
c3
 
 T T T T
(b) Create a matrix B =  c2  (The rows of matrix B are c3 , c2 , c1 ).

 
cT
1
 T T T
(c) Create a matrix C = r3 r1 r2 (The columns of matrix C are rT T T
3 , r1 , r2 ).
   
a21 a22 a11 a12
(d) Extract the matrices D = and E = from the matrix A.
a31 a32 a31 a32
Here, aij is the ijth element (row = i, column = j) of matrix A.

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