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Consider the matrix A = [[a, b, c],[d, e, f],[g, h, i]] Given the elementary matrix...

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masterpiece11 | Student | (Level 1) Salutatorian

Posted April 25, 2013 at 4:19 AM via web

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Consider the matrix

A = [[a, b, c],[d, e, f],[g, h, i]]

Given the elementary matrix

E_2= [[1, 0, 0],[0, 6, 0],[0, 0, 1]]

- Compute AE_2.

- Multiplying by E_2 on the right applies a "column operation" to A. Describe the column operation associated with E_2.

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mathsworkmusic | (Level 1) Educator

Posted May 27, 2013 at 6:12 PM (Answer #1)

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We are given that

`A = ((a,b,c),(d,e,f),(g,h,i))`

and that the elementary matrix `E_2 = ((1,0,0),(0,6,0),(0,0,1))`

(an elementary matrix is one that can be reached from the identity matrix of the same dimension by an elementary row operation).

Therefore we calculate that

`AE_2 = ((a,b,c),(d,e,f),(g,h,i))((1,0,0),(0,6,0),(0,0,1)) = ((a,6b,c),(d,6e,f),(g,6h,i))`

Multiplying by the elementary matrix E_2 on the right is equivalent then to the column operation

`C_2 -> 6C_2`

Answer: AE_2 = `((a,6b,c),(d,6e,f),(g,6h,i))`  . From this we can then see that multiplying on the right by the elementary matrix E_2 is equivalent to performing the column operation `C_2 -> 6C_2`.

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