COMP SCI 532
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practice_exam1_532 Madison COMP SCI 532|ALL THAT YOU NEED
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CS/ECE/ME 532 
Practice Midterm Exam 1 — 2021 
Each problem is 25 points. 
Name: 
1. 
2. 
3. 
4. 
(total score) 
1. Answer the following questions. Make sure to explain your reasoning. 
a. Are the columns of the following matrix linearly independent? Are they orthogonal? 
A = 
 
 
 
 
 
+0.5 +0.5 
−0.5 +0.5 
+0.5 −0.5 
−0.5 −0.5 
 
 
 
 
 
b. Are the columns of the following matrix linearly independent? 
A = 
 
 
 
+1 +1 +1 
−1 +1 −1 
+1 −1 ...
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