Show that the function T:R2-R2 defined by T(X1,X2)=(x1-X2, X1+X2) for (X1-X2) e R2 Is biyetive
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GIVEN
The linear mapping
defined by
TO PROVE
T is bijective
FORMULA TO BE IMPLEMENTED
T is said to be bijective if T is one to one and onto
EVALUATION
CHECKING FOR ONE TO ONE
Let
On addition
From
We get
Hence
Hence T is one to one
CHECKING FOR ONTO
We know that
So Im T is a linear span of
Now
Now we are proceeding to check whether
are linearly independent
Let
On addition
Now from We get
So
Therefore is linearly independent
So
Hence T is onto
RESULT
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