Question

a 0 0 where a b, and c are positive numbers. Let S be the unit ball whose bounding surface has the equation x-x R3 + R3 be a linear transformation determined by the matrix A= 1 Complete Let 0 b 0 + x 0 0 c parts a and b below. u1 x1 2 ,2 2 a Show that T S is bounded by the ellipsoid with the equation 1 Create a vector u = that is within set S and create vector x- . How should these vectors and matricies be used? + + u2 x2 u3 X3 O A. Set x equal to Au. Multiply the matrix A 1 by the vector u. O B. Set x equal to Au. Multiply the matrix A by the vector u. O C. Set A equal to xu. Multiply the vector x by vector u O D. Set u equal to Ax. Multiply the matrix A by the vector u. Perform the operation of matrices and vectors from the previous step and determine the values for u in terms of x1 x2-x3-a, b, and c. 2 How does this show that T(S) is bounded by the ellipsoid with the given equation? A. ·1 if u is in S By substituting the known values In order for u to bein set S it must follow the equation-+-+ 1 Instead of x values it would use the equivalent u values, meaning that + + of u, the resl isx21 -5าร์-1 Instead ox values ufuf-1 B 小小小'" n order fruto be insets must folow the equationx would use the equivalent u values, meaning that u u sins. By substituting the known values of u By the result is-+-+-=1 4x b. Use the fact that the volume of the unit ball isto determine the volume of the region bounded by the ellipsoid in part (a). The volume of the region is (Type an exact answer in terms of π.)

Answer 1

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