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Let P7(x) be the real vector space of polynomials, in the variable x with real coefficients and having degree at most 7, together with the zero polynomial.Let T : P7(x) β P7(π₯) be the linear transformation defined by
\(T(f(x))=f(x)+\frac{df(x)}{dx}\).
Then, which one of the following is TRUE ?
Let P7(x) be the real vector space of polynomials, in the variable x with real coefficients and having degree at most 7, together with the zero polynomial.Let T : P7(x) β P7(π₯) be the linear transformation defined by
\(T(f(x))=f(x)+\frac{df(x)}{dx}\).
Then, which one of the following is TRUE ?
\(T(f(x))=f(x)+\frac{df(x)}{dx}\).
Then, which one of the following is TRUE ?
Updated On: Oct 1, 2024
- T is not a surjective linear transformation
- There exists k β \(\N\) such that Tk is the zero linear transformation
- 1 and 2 are the eigenvalues of T
- There exists r β \(\N\) such that (T - I)r is the zero linear transformation, where I is the identity map on P7(x)
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The Correct Option is D
Solution and Explanation
The correct option is (D) : There exists r β \(\N\) such that (T - I)r is the zero linear transformation, where I is the identity map on P7(x).
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