3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and B2

Q: 3. The linear operator T: R³ R³ is defined by T(x1, x2, x3) = (W1₁, W2, W3), where w₁ = 2x₁ + 4x2 +…

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Q: 4. Consider the set of functions S = {-3(x² – 4)°,7|x² – 4|³}. a. Show that S is a linearly…

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Q: If a 2 × 2 matrix A is non-invertible, then the image of the unit square under the linear…

A: False Reason : Here the image of unit square image

Q: Let A = ū= [¹²3] a [¹3] and v u= LO [2] and define T: R² → R² by T(x) = Ax. Find the images under…

A: The given matrix  and the linear transformation .The aim is to find the images of  and .

Q: 6. Let f be entire and suppose that Re(f(z)) + Im(f(z)) ≥ 0. Show that f(z) must be a constant…

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Q: Let f:R → R such that f(x) = x² – 2x + 1. Verify whether f is bijective ? explain your answer.

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Q: Prove or disprove: If (n) and (yn) are subsequences of each other, then n = yn.

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Q: Prove that the function f: R –→ R defined by f (x) = 3x – 5 is bijective.

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Q: Let ƒ : R\{1} →→ R\{1} be defined by f(x) = x/(x - 1). Show that ƒ is bijective and find f-¹. Also,…

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Q: 23. Determine whether each of these functions is a bijection from R to R. a) f(x) = 2x + 1 b) f(x) =…

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