Consider the matrix A = [[a, b, c],[d, e, f],[g, h, i]] Given the elementary matrix E_1= [[1, 0, 3],[0, 0, 1],[0, 1, 0]] - Compute AE_1. - Multiplying by E_1 on the right applies a "column...

Consider the matrix

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

Given the elementary matrix

E_1= [[1, 0, 3],[0, 0, 1],[0, 1, 0]]

- Compute AE_1.

- Multiplying by E_1 on the right applies a "column operation" to A. Describe the column operation associated with E_1.

Asked on by blasto63

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mathsworkmusic | (Level 2) Educator

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We have

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

and `E_1 = ((1,0,3),(0,0,1),(0,1,0))`

Therefore `AE_1 = ((a,b,c),(d,e,f),(g,h,i))((1,0,3),(0,0,1),(0,1,0)) = ((a,c,3a+b),(d,f,3d+e),(g,i,3g+h))`

We can see that the column operation given by multiplying by `E` on the right is

`C_2 -> C_3`  and `C_3 -> 2C_1 + C_2`

AE_1 = `((a,c,3a+b),(d,f,3d+e),(g,i,3g+h))` and multiplying on the right by E is equivalent to the column operations `C_2 -> C_3` and `C_3 -> 2C_1 + C_2`.

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