Which of the following matrices is elementary matrix? a) begin{bmatrix}0 & 3 1 & 0 end{bmatrix} b) begin{bmatrix}2 & 0 0 & 1 end{bmatrix} c) begin{bmatrix}1 & 0 0 & 1 end{bmatrix} d) begin{bmatrix}2 & 0 0 & 2 end{bmatrix}

Elleanor Mckenzie 2020-11-08 Answered
Which of the following matrices is elementary matrix?
a) [0310]
b) [2001]
c) [1001]
d) [2002]
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Expert Answer

FieniChoonin
Answered 2020-11-09 Author has 102 answers
Step 1
Since your question has multiple subparts we have solved the first three subparts for you.
Identify the elementary matrices
Elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation.
a) [0310]
Apply minimum elemantary row operation on identity matrix to form this matrix.
[1001]
R1R2
[0110]
R13R1
[0310]
Since the matrix is formed by applying two elementary row operations therefore it is not an elementary matrix.
Step 2
Similarly check other matrices
b) [2001]
[1001]
R1R1
[1001]
Since [1001] differs the identity matrix by one elementary operation hence it is an elementary matrix.
Step 3 Similarly check other matrices
c) [1001]
[2001]
R12R1
[2001]
Since [2001] differs the identity matrix by one elementary operation hence it is an elementary matrix.
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Jeffrey Jordon
Answered 2022-01-27 Author has 2047 answers

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