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Department of Computer Science and Engineering

1st Mid Exam

Course Title: Complex Variable and Matrices (MATH -2109)

Semester: 3rd | Session: 19-20

Time: 45 minutes | Marks: 10.00

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Answer only one question from each Part A & Part B according to the directions.

1.
Scenario:

(A) [Take remainder after dividing your ID's last two digits by 3.]

0)

Show that A = 

1/9  8/9  -4/9
4/9  -4/9  -7/9
8/9  1/9  4/9

is an orthogonal matrix. Also show that row vectors of A are orthonormal to each other.
 

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1)

Show that

is an orthogonal matrix.

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2)

For 

   ,

what can we say about the matrices A-1, B-1, AB and BA. Verify your claim by calculation.

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2.
Scenario:

(B) [Take remainder after dividing your ID's last two digits by 3.]
 

0)

Show that

is a normal matrix. 

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1)

Show that

is a unitary matrix. Find A-1.

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2)

Show that

is a nilpotent matrix. What is its index? Find (1 - A)-1.

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Uploaded By: Onebyzero Edu July 28, 2024, 3:45 p.m.
Converted By (Img/PDF to Text): Baishakhi Bir Feb. 27, 2026, 7:24 p.m.
Reviewed By: Obaydul Hasan Nayeem March 1, 2026, 2:15 p.m.