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Let T be a linear transformation such that T(v) = Av. Find A such that T(v) = Av.

User Tong
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Final answer:

To find the matrix A in a linear transformation T(v) = Av, where A is a constant matrix and v is a vector, we equate the two equations and simplify to find that 0 = 0. Hence, there are multiple matrices A that can satisfy the given condition.

Step-by-step explanation:

Let's assume that T is a linear transformation. We are given that T(v) = Av, where A is a constant matrix and v is a vector. To find A, we can equate the two equations:

T(v) = Av

Since T(v) = Av, we can rewrite it as T(v) - Av = 0. Now, let's expand it further:

Av - Av = 0. As a result, 0 = 0.

From this equation, we can't determine the value of A, as any matrix multiplied by the vector v will give 0. Hence, there are multiple matrices A that can satisfy the given condition.

User Mr Sam
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