Written Assignment Question 2? Please solve in details.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 23EQ
icon
Related questions
icon
Concept explainers
Topic Video
Question
Written Assignment Question 2? Please solve in details.
3:22
A ll 12%I
2.1 Matrix Operations sp 20.pdf
Theorem 2.1.2: Properties of Matrix Multiplication
Let A be an m xa matrix, and let B and C have sizes for which the indicated
sums and products are defined.
a. A(BC) = (AB)C
b. A(B +C) = AB + AC
c. (B+C)A = BA + CA
d. r(AB) = (rA)B- ArB)
for any scalar r
e. ImA = A = Al,
(associative law of multiplication)
(left distributive law)
(right distributive law)
(identity for matrix multiplication)
III.
Transpose of a Matrix
DEFINITION: Transpose of a Matrix
Given an m xn matrix A, the transpose of A, denoted A", is defined to be an n x m matrix
created by rewriting the rows of A as columns.
Example 5:
Find the transpose of the matrix A =:
2
Solution:
AT
Theorem 2.1.3: Properties of the Transpose of a Matrix
Let A and B denote matrices whose sizes are appropriate for the following sums
and products.
a. (A) = A
b. (A+ B) = A + B
c. For any scalar r. (rA) - rA
d. (AB) - BA
Now try Written Assignment, Question 2:
Solve for A, given that B = 3 :
Transcribed Image Text:3:22 A ll 12%I 2.1 Matrix Operations sp 20.pdf Theorem 2.1.2: Properties of Matrix Multiplication Let A be an m xa matrix, and let B and C have sizes for which the indicated sums and products are defined. a. A(BC) = (AB)C b. A(B +C) = AB + AC c. (B+C)A = BA + CA d. r(AB) = (rA)B- ArB) for any scalar r e. ImA = A = Al, (associative law of multiplication) (left distributive law) (right distributive law) (identity for matrix multiplication) III. Transpose of a Matrix DEFINITION: Transpose of a Matrix Given an m xn matrix A, the transpose of A, denoted A", is defined to be an n x m matrix created by rewriting the rows of A as columns. Example 5: Find the transpose of the matrix A =: 2 Solution: AT Theorem 2.1.3: Properties of the Transpose of a Matrix Let A and B denote matrices whose sizes are appropriate for the following sums and products. a. (A) = A b. (A+ B) = A + B c. For any scalar r. (rA) - rA d. (AB) - BA Now try Written Assignment, Question 2: Solve for A, given that B = 3 :
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
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 and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning