# 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

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.

#### 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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