Let a11 a12 a13 A = a21 a22 a23 a31 a32 a33 3 x 3 real matrix and consider it as a linear map A: R³ R³ oute ^³(A) : ^³(R³) → ^³(R³) with respect to the standard basis of R³ and verify sual formula for the determinant of a 3 × 3 matrix holds

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
icon
Related questions
Question

note the inverted wedge is (lambda). 

Let
a11 a12 a13
a21 a22 a23
a31 a32 a33
be a 3 x 3 real matrix and consider it as a linear map
A: R³ R³
Compute A³(A): ^³(R³) → ^³(R³) with respect to the standard basis of R³ and verify that
the usual formula for the determinant of a 3 × 3 matrix holds
A =
Transcribed Image Text:Let a11 a12 a13 a21 a22 a23 a31 a32 a33 be a 3 x 3 real matrix and consider it as a linear map A: R³ R³ Compute A³(A): ^³(R³) → ^³(R³) with respect to the standard basis of R³ and verify that the usual formula for the determinant of a 3 × 3 matrix holds A =
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
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
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