MANE 3351

Lecture 21

Classroom Management

Agenda

• Inverting Matrices by Hand
• Transpose of a Matrix
• Python for Linear Algebra
• Homework 6
• Lab 9 for those who did not finish on Monday

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Resources

Handouts

• Lecture 21 slides
• Lecture 21 slides marked
• Python Linear Algebra Cheat Sheet

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Calendar

Week	Monday Lecture	Wednesday Lecture
12	11/17: Lecture 21	11/19: Lecture 22
13	11/24: Lecture 23	11/26: Lecture 24
14	12/1: Lecture 25	12/3: Lecture 26
15	12/8: Lecture 27	12/10: Review

Final Exam is Monday 12/15/2025 8:00 - 9:45 AM

I will be off-campus participating in an ABET visit and a proctor will be arranged for the final exam.

Assignments

• Homework 6 (assigned 11/17, due 11/24)
• Lab Assignment 8 (assigned 11/12/25, due 11/19/25 before 9:30 AM)

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Inverting 2 x 2 Matrices by Hand

• Inverting 2x2

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Ex: Inverting a 2x2 Matrix by Hand

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Inverting 3x3 Matrices by Hand

• Inverting 3x3

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Ex: Inverting a 3x3 Matrix by Hand

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Transpose of a Matrix

• Matrix Transpose

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Python Linear Algebra Cheat Sheet

• Jupyter Notebook Demonstration

import numpy as np
from scipy import linalg, sparse
# Creating matrices

A=np.mat([[3,4],[5,6]])
print(A)

print(A.I)
print(linalg.inv(A))

print( A.I @ A)

C=np.mat([[1,2,5],[5,8,2],[7,6,5]])
print(C)

rhs = ([4],[25],[-3])
print(rhs)

print(C.I @ rhs)
print(linalg.solve(C,rhs))

print(A.T)

print(linalg.det(C))

D= np.matrix(np.random.random((2,2)))
print(D)