66. Proof Complete the proof of Theorem 2.3. (a) Prove the associative property of multiplication: A(BC) = (AB)C. (b) Prove the distributive property: (A + B)C = AC + BC. (c) Prove the property:

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 17E
icon
Related questions
Question

Don't give handwritten answer....

66. Proof Complete the proof of Theorem 2.3.
(a) Prove the associative property of multiplication:
A(BC) = (AB)C.
(b) Prove the distributive property:
(A + B)C= AC + BC.
(c) Prove the property:
c(AB) = (cA)B = A(cB).
Transcribed Image Text:66. Proof Complete the proof of Theorem 2.3. (a) Prove the associative property of multiplication: A(BC) = (AB)C. (b) Prove the distributive property: (A + B)C= AC + BC. (c) Prove the property: c(AB) = (cA)B = A(cB).
THEOREM 2.3 Properties of Matrix Multiplication
If A, B, and C are matrices (with sizes such that the matrix products are defined),
and c is a scalar, then the properties below are true.
1. A(BC) = (AB)C
2. A(B+C) = AB + AC
3. (A + B)C = AC + BC
4. c(AB) = (CA)B = A(CB)
Associative property of multiplication
Distributive property
Distributive property
Transcribed Image Text:THEOREM 2.3 Properties of Matrix Multiplication If A, B, and C are matrices (with sizes such that the matrix products are defined), and c is a scalar, then the properties below are true. 1. A(BC) = (AB)C 2. A(B+C) = AB + AC 3. (A + B)C = AC + BC 4. c(AB) = (CA)B = A(CB) Associative property of multiplication Distributive property Distributive property
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage