20. Let A = (a;j) be a given (3 × 3) matrix. Form the associated (3 x 5) matrix B shown next: a12 B = | a21 a22 a) Subtract the sum of the three upward diagonal products from the sum of the three downward diagonal products and argue that your result is equal to det(A). b) Show, by example, that a similar basketweave algorithm cannot be used to calculate the determinant of a (4 × 4) matrix.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 77E
icon
Related questions
Question
solve the question with complete neat explanation within 10 mins and get upvotes
20. Let A = (a;;) be a given (3 × 3) matrix. Form the
associated (3 × 5) matrix B shown next:
d12
B = | a21
a22
a32
a) Subtract the sum of the three upward diagonal
products from the sum of the three downward
diagonal products and argue that your result is
equal to det(A).
b) Show, by example, that a similar basketweave
algorithm cannot be used to calculate the
determinant of a (4 × 4) matrix.
Transcribed Image Text:20. Let A = (a;;) be a given (3 × 3) matrix. Form the associated (3 × 5) matrix B shown next: d12 B = | a21 a22 a32 a) Subtract the sum of the three upward diagonal products from the sum of the three downward diagonal products and argue that your result is equal to det(A). b) Show, by example, that a similar basketweave algorithm cannot be used to calculate the determinant of a (4 × 4) matrix.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
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
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