Let T be linear transformation oninto itself such that T(1,0) = (1,2) and T (1, 1) = (0, 2) .Then T(a, b) is equal toa)(a, 2b)b)(2a, b)c)(a - b, 2a) d)(a - b, 2b)Correct answer is option 'C'. Can you explain this answer?

Question

Answer

As {(1,0),(1,1)} form a basis for R^2 so, (a,b) can be written as Linear combination of (1,0) &(1,1).

(a,b) = (a-b)(1,0) + b(1,1)

So, T(a,b) = T(b(1,1) + (a-b)(1,0))
= b T(1,1) + (a-b) T(1,0)
= b (0,2) + (a-b) (1,2)
= (a-b, 2a) [Option C]

Answer

To keep here and degree and so emergent ,
ans is c

Answer

To find T(a, b), we can express (a, b) as a linear combination of (1,0) and (1,1) using the given information.

- Expressing (a, b) as a linear combination: (a, b) = a(1,0) + b(0,1) = a(1,0) + b(1,1) - b(1,0)
- Using the given values: T(a, b) = aT(1, 0) + bT(1, 1) - bT(1, 0)
- Substituting the given values for T(1, 0) and T(1, 1): T(a, b) = a(1, 2) + b(0, 2) - b(1, 2)
- Simplifying the expression: T(a, b) = (a, 2a) - (b, 2b) = (a - b, 2a)
Therefore, the correct answer is C: (a - b, 2a).

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