Consider the matrix

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

For each of the following elementary matrices E,

E_3 =[[1, 0, 0],[0, 0, 1],[0, 1, 0]]

Compute AE.

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

### 1 Answer | Add Yours

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

For each of the following elementary matrices E,

E_3 =[[1, 0, 0],[0, 0, 1],[0, 1, 0]]

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

`E_3=[[1,0,0],[0,0,1],[0,1,0]]`

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

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

`E_3A=[[1,0,0],[0,0,1],[0,1,0]][[a,b,c],[d,e,f],[g,h,i]] `

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

`R_2<- >R_3` (interchanged)

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