Jump to level1 (E) x1 x2 Let T : R? → R² be defined by T X2 x1 -- (} 8 and C = Let u V1 = , V2 = Find T(u), the image of u under T. Find [T(u)]c, the coordinatization of T(u) with respect to the basis C. Ex: 5 T(u) = [T(u)]c 1 4 Check Next

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Q: (b) The square with vertices (0,0), (1, 0), (1, 1) and (0, 1), and the vector field F = 3x²yi + x³j.

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Q: Let B = {v1,...,Vn} be an orthonormal basis for R". (a) Prove Parseval's Identity, that is, for any…

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Q: ,T If {v1, ..., Vn} is an orthonormal basis for R", then vịv¡ + · · ·+ vn Vn = I. True False

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Q: 5. Find the standard matrix for the linear operator T: R3 → R3 that first transform by the formula…

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Q: Let C := {1, cos t, cos 2t, cos 6t} C V ...) where V is the vector space of all real-valued…

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Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

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Q: Let V = Poly4(R) and let B = (1, x2 − 1, x, x^3 − 2x, x^4 − 3x^2 + 1). (a) Find a basis C of V such…

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Q: Take L: V --> W, from P2 --> P2 and L(p) = p + p', with basis B = {1 + x + x2, 1 + x, 2x + x2} and…

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Q: (:) - Let T : R? → R² be defined byT X2 X1 – x2 - 2 and C = 6. Let u = Vị = ,V2 = Find T(u), the…

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Q: If f(x) = x^2 + 7x+2, g(x) = x^2 - x + 1 find a polynomial h(x) of degree 2 such that together these…

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Q: 1.Assume (f,g) = | f(x)g(x)dx is the inner product for V = P, . Apply the Gram-Schmidt process to…

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Q: Explain why S is not a basis for R2. S - {(-5, 2)} O sis linearly dependent. O s does not span R2. O…

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Q: |– 1/V5 29) Let u,= 2/ 5 2/V5 [1/v5] Show that {u1,u,} is an orthonormal basis for R².

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Q: 10)Define TE L(R²) by T(x, y) = (41x + 7y,-20x + 74y). Verify that the basis of T %3D with respect…

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