Find the canonical form for the following 2nd order surface 2. (22 + y,+ ) +5 (ay+ az+ yz) +- 2y+4z+1= 0 Write the matrix of rotation C for the canonical change of coordinates T = CE and the values (81, 82, 83) for the shift 元=十81 ý = j + 82 ミ=2+ 83

Q: Describe all solutions of Ax = b, where 2-5 3 A -2 6 -5 70] and b = Describe the general solution in…

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Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

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A: a). b).

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A: We use the definition of coordinate vector relative to a given basis to answer the given question.

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Q: what if it was the same vector, but 5y^2j?

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A: Let us consider a vectora→ = a1i^ +a2j^ +a3k^where a1 , a2, a3 are functions of (x1, x2 & x3)and…

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A: In two dimensions, the standard rotation matrix has the following form:

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Q: Calculate the dot product of u = (-4, -2, 7, -2) and v = (-3, 1,5,8). u. V =

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