Let A and B be A=[10−231010−3], B=[10−331010−2] Find an elementary matrix E such that EA=B.

The given matrices are A=[10−231010−3], B=[10−331010−2] Note that the matrix A can be obtained by interchanging the rows R1 and R3 of B. Perform the same operation in I=[100010001] and obtain that R=[001010100] Check the condition as follows. EA=[001010100][10−231010−3] =[10−331010−2] =B Thus , the required elementary matrix is E=[001010100]

Expert Answer to "Let A and B be A=[10−231010−3], B=[10−331010−2] Find..."

High School
Other

Edmund Conti

Answered question

2021-11-14

Let A and B be

A = [\begin{matrix} 1 & 0 & - 2 \\ 3 & 1 & 0 \\ 1 & 0 & - 3 \end{matrix}], B = [\begin{matrix} 1 & 0 & - 3 \\ 3 & 1 & 0 \\ 1 & 0 & - 2 \end{matrix}]

Find an elementary matrix E such that EA=B.

Answer & Explanation

Phisecome

Beginner2021-11-15Added 18 answers

The given matrices are $A = [\begin{matrix} 1 & 0 & - 2 \\ 3 & 1 & 0 \\ 1 & 0 & - 3 \end{matrix}], B = [\begin{matrix} 1 & 0 & - 3 \\ 3 & 1 & 0 \\ 1 & 0 & - 2 \end{matrix}]$
Note that the matrix A can be obtained by interchanging the rows $R_{1}$ and $R_{3}$ of B.
Perform the same operation in $I = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ and obtain that $R = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}]$
Check the condition as follows.
$E A = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}] [\begin{matrix} 1 & 0 & - 2 \\ 3 & 1 & 0 \\ 1 & 0 & - 3 \end{matrix}]$
$= [\begin{matrix} 1 & 0 & - 3 \\ 3 & 1 & 0 \\ 1 & 0 & - 2 \end{matrix}]$
$= B$
Thus , the required elementary matrix is $E = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}]$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Other

Didn't find what you were looking for?