Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Algebra Matrix Representation of Linear Transformations
Consider the vector space ℙn of real polynomials in x of degree less than or equal to n. Define T : ℙ2 → ℙ3 by (Tf) (x) = \(\int_0^x f(t) d t+f^{\prime}(x)\) Then the matrix representation of T with respect to the bases (1, x, x2) and (1, x, x2, x3) is
1
\(\left(\begin{array}{llll} 0 & 1 & 0 & 0 \\ 1 & 0 & \frac{1}{2} & 0 \\ 0 & 2 & 0 & \frac{1}{3} \end{array}\right)\)
2
\(\left(\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & \frac{1}{3} \end{array}\right)\)
3
\(\left(\begin{array}{llll} 0 & 1 & 0 & 0 \\ 1 & 0 & 2 & 0 \\ 0 & \frac{1}{2} & 0 & \frac{1}{3} \end{array}\right)\)
4
\(\left(\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & \frac{1}{2} \\ 0 & 2 & 0 \\ 0 & 0 & \frac{1}{3} \end{array}\right)\)
5
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