Analysis of Linear Transformation T
Linear transformation T:R^2 to R^2 is defined by T(x) = M(x), where M = (1 1)(2 1)(-1 -3).

Determine Range of T
To find the range of T, we need to determine all possible values of T(x) for any vector x in R^2. Since T(x) = M(x), we can express T(x) in terms of matrix multiplication as T(x) = Mx.

Matrix Multiplication
Multiplying the matrix M by a vector x = (a, b), we get:
T(x) = Mx
= (1 1)(2 1)(-1 -3)(a)(b)
= (a + b)(2a + b)(-a - 3b)

Range of T
The range of T is the set of all possible outputs of T(x) for all vectors x in R^2. Therefore, the range of T is the set of all vectors of the form (a + b, 2a + b) where a and b are real numbers.

Determining Vectors in Range of T
To determine which of the following vectors can not be in the range of T, we need to check if each vector can be expressed in the form (a + b, 2a + b) for some real numbers a and b.

Vectors in Question
Let's consider the following vectors:
1. (3, 4)
2. (0, 1)
3. (1, -2)
4. (2, 5)

Analysis
- Vector (3, 4):
Can be expressed as (3 + 4, 2*3 + 4) = (7, 10)
Therefore, (3, 4) can be in the range of T.
- Vector (0, 1):
Can be expressed as (0 + 1, 2*0 + 1) = (1, 1)
Therefore, (0, 1) can be in the range of T.
- Vector (1, -2):
Can be expressed as (1 + (-2), 2*1 + (-2)) = (-1, 0)
Therefore, (1, -2) can be in the range of T.
- Vector (2, 5):
Can be expressed as (2 + 5, 2*2 + 5) = (7, 9)
Therefore, (2, 5) can be in the range of T.

Conclusion
All of the given vectors can be in the range of T as they can be expressed in the form (a + b, 2a + b) for some real numbers a and b.