32. (a) Suppose that A and B are the matrices of Example 5. Show that (A + B)² # A² + 2AB + B². (b) Suppose that A and B are square matrices such that AB = BA. Show that (A + B)2 = A² + 2AB + B².
32. (a) Suppose that A and B are the matrices of Example 5. Show that (A + B)² # A² + 2AB + B². (b) Suppose that A and B are square matrices such that AB = BA. Show that (A + B)2 = A² + 2AB + B².
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Do 32 pls
Transcribed Image Text:Problems 31-38 illustrate ways in which the algebra of matri-
ces is not analogous to the algebra of real numbers.
31. (a) Suppose that A and B are the matrices of Example 5.
Show that (A + B) (A − B) ‡ A² – B².
(b) Suppose that A and B are square matrices with the
property that AB = BA. Show that (A+B) (A - B) =
A²-B².
32. (a) Suppose that A and B are the matrices of Example 5.
Show that (A + B)² ★ A² + 2AB + B².
(b) Suppose that A and B are square matrices such that
AB=BA. Show that (A + B)² = A² + 2AB + B². T
Transcribed Image Text:In Problems 5-12, two matrices A and B are given. Calculate
whichever of the matrices AB and BA is defined.
5. A =
2
3
2
B =
-4 2
13
Expert Solution
Step 1
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning