5. Find the standard matrix for the linear operator T: R³ R³ that first transform by the formula T(x, y, z) = (x-y+z, -x + y, y-z), then rotate the resulting vector anti clockwise about the z-axis through an angle = 120°, and then project the resulting vector about zx-plane. Hence compute T(1,0,1).

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A: The answer is given below:

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A:

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A: Dear student as per our guidelines we can solve only first 3 questions. So kindly resubmit remaining…

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Q: Let T: R² R² be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps v = (1,…

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Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

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Q: Show that the vectors a, (1, 0, 0), a2 = (1, 1,0), a, = (1, 1, 1) form a basis of C'(C).

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Q: The third column of the change of basis matrix from the basis B = [u= (1,1,1); v = (1,0,1); w=…

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Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R² R², T(x, y) = (2y,…

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