Prove that there is an equivalent set of properties of determinants for column operations as there are for row operations. Complete the proof for each property on 3x3 matrices. [Hint: you may find using elementary matrices to be of help. To perform column operations with elementary matrices, multiply on the right instead of the left.] a. Exchanging two rows of a matrix changes the sign of the determinant. b. Adding two rows of a matrix does not change the value of the determinant. c. Multiplying one row of a matrix by the scalar k changes the value of the determinant by k.
Prove that there is an equivalent set of properties of determinants for column operations as there are for row operations. Complete the proof for each property on 3x3 matrices. [Hint: you may find using elementary matrices to be of help. To perform column operations with elementary matrices, multiply on the right instead of the left.] a. Exchanging two rows of a matrix changes the sign of the determinant. b. Adding two rows of a matrix does not change the value of the determinant. c. Multiplying one row of a matrix by the scalar k changes the value of the determinant by k.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 3AEXP
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![8. Prove that there is an equivalent set of properties of determinants for column operations as
there are for row operations. Complete the proof for each property on 3x3 matrices. [Hint: you
may find using elementary matrices to be of help. To perform column operations with
elementary matrices, multiply on the right instead of the left.]
a. Exchanging two rows of a matrix changes the sign of the determinant.
b. Adding two rows of a matrix does not change the value of the determinant.
c. Multiplying one row of a matrix by the scalar k changes the value of the determinant by k.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F410816ed-4be2-4291-b0fb-4c8f4b2206ab%2F4924b857-b0bd-4c5c-bdcf-b30c2fe8f9e2%2Fm3p27kd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. Prove that there is an equivalent set of properties of determinants for column operations as
there are for row operations. Complete the proof for each property on 3x3 matrices. [Hint: you
may find using elementary matrices to be of help. To perform column operations with
elementary matrices, multiply on the right instead of the left.]
a. Exchanging two rows of a matrix changes the sign of the determinant.
b. Adding two rows of a matrix does not change the value of the determinant.
c. Multiplying one row of a matrix by the scalar k changes the value of the determinant by k.
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