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Question 3.1. Let's think of the set of n-by-n matrices as R² by using the matrix entries as coordinates. Let DC R² be the subset of matrices with determinant zero. Select all the statements which are true. (a) The subset D is closed under rescaling. (b) The subset D is closed under addition. (c) The subset D contains the origin. (d) The subset D is an affine subspace.

Question 3.1. Let's think of the set of n-by-n matrices as R² by using the matrix entries as coordinates. Let DC R² be the subset of matrices with determinant zero. Select all the statements which are true. (a) The subset D is closed under rescaling. (b) The subset D is closed under addition. (c) The subset D contains the origin. (d) The subset D is an affine subspace.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 3.1. Let's think of the set of n-by-n matrices as R by using the matrix entries as coordinates. Let D C R² be the subset of matrices with determinant zero. Select all the statements which are true. (a) The subset D is closed under rescaling. (b) The subset D is closed under addition. (c) The subset D contains the origin. (d) The subset D is an affine subspace. Select all the statements which are true.. explain the reason why they are true?
Transcribed Image Text:Question 3.1. Let's think of the set of n-by-n matrices as R by using the matrix entries as coordinates. Let D C R² be the subset of matrices with determinant zero. Select all the statements which are true. (a) The subset D is closed under rescaling. (b) The subset D is closed under addition. (c) The subset D contains the origin. (d) The subset D is an affine subspace. Select all the statements which are true.. explain the reason why they are true?
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