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Apply the given elementary transformation of the following matrix. A = [1-13210331], 3R3 and then C3 + 2C2 and A = [1-13210331], C3 + 2C2 and then 3R3What do you conclude. - Mathematics and Statistics

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Sum

Apply the given elementary transformation of the following matrix.

A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R3 and then C3 + 2C2

and A = `[(1,-1,3),(2,1,0),(3,3,1)]`, C3 + 2C2 and then 3R3
What do you conclude.

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Solution

A = `[(1,-1,3),(2,1,0),(3,3,1)]`

By 3R3, we get,

A ∼ `[(1,-1,3),(2,1,0),(9,9,3)]`

By C3 + 2C2, we get,

A ∼ `[(1,-1,3+2(-1)),(2,1,+2(1)),(9,9,+2(9))]`

∴ A ∼ `[(1,-1,1),(2,1,2),(9,9,21)]` ..............(i)

And

A = `[(1,-1,3),(2,1,0),(3,3,1)]`

By C3 + 2C2, we get,

A ∼ `[(1,-1,3+2(-1)),(2,1,0+2(1)),(3,3,+1+2(3))]`

∴ A ∼ `[(1,-1,1),(2,1,2),(3,3,7)]`

∴ A ∼ `[(1,-1,1),(2,1,2),(3,3,7)]`

By 3R3, we get

A ∼ `[(1,-1,1),(2,1,2),(9,9,21)]` ......(ii)

We conclude from (i) and (ii)  the matrix remains the same by interchanging the order of the elementary transformations. Hence, the transformations are commutative.

Concept: Elementry Transformations
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