Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Linear Algebra Algebra of Linear Transformations
Let P be the vector space (over ℝ) of all polynomials of degree ≤ 3 with real coefficients. Consider the linear transformation T : P → P defined by T(a0 + a1x + a2x2 + a3x3) = a3 + a2x + a1x2 + a0x3. Then the matrix representation M of T with respect to the ordered basis {1, x, x2, x3} satisfies
1
M2 + I4 = 0
2
M2 - I4 = 0
3
M - I4 = 0
4
M + I4 = 0
5
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