Let T: R² →R² be a linear transformation that maps u = the fact that T is linear to find the image of 2u + v. A. 8 12 Ов. 2 ○ D. -6 12 - 16 4 -12 5 into and maps v = 5 [:] [10] [2] -2 into 이 -8 Use 4

Which of the following transformations are linear? yi X] + 10 y2 X2 8x1 Yı 7 y2 3x1 + x2 C. -Xi 0. y2 D. 9x2 %3D y2 E.3 y2 Уз 3 X1 7x1 – 2x2 + 6x3 y2 = 10x2 - 3x3 -4x1 – 9x2 F.- Y3 = |L || || || I| || || || IL || || || A. B.

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Determine whether the function L: P2 → P2 defined by L(a0 +a1x+a2x2) = a1 +2a2xis a linear transformation. Explain, and show all your work.

Give one application of linear transformation then explain while including illustrations for support.

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Please explain how you know the transformation is linear or not! Thank you! Which of the following transformations are linear? yi А. y2 X1X2 %3D В. y2 X3 %3D Y3 X1 %3D Yi 2x1 – 5x2 + 3x3 %3D С. y2 6x2 – 4x3 %3D Уз -10x1 – 8x2 yi 4 D. y2 8. = Уз 10 yi 4x1 + x2 'E. Y2 -X1 -3x1 = yi F. y2 5x1 %3D Уз 9x1 %3D I| ||||

Form a transformation T such that T: R^5 → R^5. Check the transformation is linear or not. Also verify existence of inverse transformation for your example

Help me solve this linear algebra problem to review for my test.

Let T1 : P2 → R² and T2 : R? → R2x2 be linear transformations defined as follows. a + b b - T1(ax? + bx + c) 1. () - 6x1 -9x1 T2 2x2 -4x2 Ex: 42 (Т, о Ti) (4а? + 5ӕ + 2)