Lect5 - Chapter 1. Matrices and Systems of Equations...

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Identity Matrices Example . Let I be the 3 × 3 identity matrix, i.e. I = 1 0 0 0 1 0 0 0 1 . Evaluate IA and AI where A = 3 4 1 2 6 3 0 1 8 .
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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Identity Matrices Example . Let I be the 3 × 3 identity matrix, i.e. I = 1 0 0 0 1 0 0 0 1 . Evaluate IA and AI where A = 3 4 1 2 6 3 0 1 8 . Example . Let e i be the i th column of the n × n identity matrix. Suppose A is an m × n matrix. What is A e i ?
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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrix Inversion - Motivation Warning Matrix multiplication is not commutative. i.e. AB 6 = BA in general. The concept of division is not introduced.
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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrix Inversion - Motivation Warning Matrix multiplication is not commutative. i.e. AB 6 = BA in general. The concept of division is not introduced. Question: What is division? Ans. 6 ÷ 2 = 3 or 6 2 = 3 means 6 = 2 × 3 = 3 × 2 .
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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrix Inversion - Motivation Warning Matrix multiplication is not commutative. i.e. AB 6 = BA in general. The concept of division is not introduced. Question: What is division? Ans. 6 ÷ 2 = 3 or 6 2 = 3 means 6 = 2 × 3 = 3 × 2 . However, AB may not equal BA in matrices!
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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrix Inversion - Motivation Warning Matrix multiplication is not commutative. i.e. AB 6 = BA in general. The concept of division is not introduced. Question: What is division? Ans. 6 ÷ 2 = 3 or 6 2 = 3 means 6 = 2 × 3 = 3 × 2 . However, AB may not equal BA in matrices! View 6 2 as 6 × 2 - 1 .
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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrix Inversion - Motivation Warning Matrix multiplication is not commutative. i.e. AB 6 = BA in general. The concept of division is not introduced. Question: What is division? Ans. 6 ÷ 2 = 3 or 6 2 = 3 means 6 = 2 × 3 = 3 × 2 . However, AB may not equal BA in matrices! View 6 2 as 6 × 2 - 1 . Question: Can we define a concept like reciprocal for matrices?
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Math1111 Matrix Algebra Matrix Inversion - Motivation Warning Matrix multiplication is not commutative. i.e. AB 6 = BA in general. The concept of division is not introduced. Question: What is division? Ans. 6 ÷ 2 = 3 or 6 2 = 3 means 6 = 2 × 3 = 3 × 2 . However, AB may not equal BA in matrices! View 6 2 as 6 × 2 - 1 . Question: Can we define a concept like reciprocal for matrices? What is reciprocal of a number?
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Lect5 - Chapter 1. Matrices and Systems of Equations...

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