# Give the correct answer and solve the given equation V = T(m, n), The set of lineartrans formations T : R^{m} rightarrow R^{n}, together with the usualadditionand scalar multiplication of functions.

Give the correct answer and solve the given equation
The set of lineartrans formations

together with the usualadditionand scalar multiplication of functions.
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Gennenzip
Given that,
The set of lineartrans formations

together with the usualadditionand scalar multiplication of functions.
Find in the following that V is a vector space.
Since the definition of linear transformation is,
If a function T defined in the following,

satisfy the following properties,
1.
2.
for all in U and alpha is any scalar
Then, T is called linear transformation.
Therefore, using these properties in the given function.

Assume,
is any scalar.
Then
1.
2. Therefore, from above shows that all properties of linear transformation satisfy.
So, is vector space with the usual addition and scalar multiplication.
Hence, V is a vector space with the usual addition and scalar multiplication.