# Consider the matrix A = [[a, b, c],[d, e, f],[g, h, i]] For each of the following elementary matrices E, E_2= [[1, 0, 0],[0, 6, 0],[0, 0, 1]] - Compute AE. - Multiplying by E on the right applies a...

Consider the matrix

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

For each of the following elementary matrices E,

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

- Compute AE.

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

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### 1 Answer

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

For each of the following elementary matrices E,

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

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

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

`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]]`

`E_2A=[[1,0,0],[0,6,0],[0,0,1]][[a,b,c],[d,e,f],[g,h,i]]`

`=[[a,b,c],[6d,6e,6f],[g,h,i]]`

`R_2->6R_2`