Mathematics · Linear Algebra
For a variable x, consider the real vector space V = {ax3 + bx2 + cx + d | a, b, c, d ∈ ℝ}. Let D: V → V be the linear transformation where D(f) is the derivative of f with respect to x, and M: V → V be the linear transformation defined by M(f) = xD(f). Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1rank(DM) > rank(MD)
- 2DM is invertible
- 3D + M is invertible
- 4DM ≠ MD✓
Correct answer
DM ≠ MD
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