Which of the following subsets of R3x3 are subspaces of R³x3 -0- 0 A. The 3 x 3 matrices A such that the vector B. The 3 x 3 matrices in reduced row-echelon form C. The 3 x 3 matrices of rank 1 is in the kernel of A

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
icon
Related questions
Question
100%
Which of the following subsets of R³x3 are subspaces of R³x³
A. The 3 x 3 matrices A such that the vector 0 is in the kernel of A
B. The 3 x 3 matrices in reduced row-echelon form
C. The 3 x 3 matrices of rank 1
D. The invertible 3 x 3 matrices
E. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries)
OF. The 3 x 3 matrices with all zeros in the second row
Transcribed Image Text:Which of the following subsets of R³x3 are subspaces of R³x³ A. The 3 x 3 matrices A such that the vector 0 is in the kernel of A B. The 3 x 3 matrices in reduced row-echelon form C. The 3 x 3 matrices of rank 1 D. The invertible 3 x 3 matrices E. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) OF. The 3 x 3 matrices with all zeros in the second row
Expert Solution
steps

Step by step

Solved in 4 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
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,