Find the characteristics and characteristic coordinates, and reduce the following equations to canonical form: (a) Urx...
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Find the characteristics and characteristic coordinates, and reduce the following equations to canonical form: (a) Urx + 2xy + 3y +4₂ +5uy+u = e², (b) 2uz-4uzy +2uyy +3u = 0, Uzz +5Uxy + 4y +7uy = sinx, (d) Uzz + Uyy + 2U₂ + 8uy+u = 0, (e) uzy +2uyy +9uz + uy = = 2, (f) 6uzx-Uxy +U=y², (g) ury + ₂ + y = 3x, (h) uyy-9uz +7uy = cos y, (i) z²ux-y²uy-U₂=1+2y², (j) uxx + yuyu+uy + 4yu, = 0. (k) r²y²uzz +2ryuzy + Uyy= = 0, (1) Uzz + yuyy <= 0. Find the characteristics and characteristic coordinates, and reduce the following equations to canonical form: (a) Urx + 2xy + 3y +4₂ +5uy+u = e², (b) 2uz-4uzy +2uyy +3u = 0, Uzz +5Uxy + 4y +7uy = sinx, (d) Uzz + Uyy + 2U₂ + 8uy+u = 0, (e) uzy +2uyy +9uz + uy = = 2, (f) 6uzx-Uxy +U=y², (g) ury + ₂ + y = 3x, (h) uyy-9uz +7uy = cos y, (i) z²ux-y²uy-U₂=1+2y², (j) uxx + yuyu+uy + 4yu, = 0. (k) r²y²uzz +2ryuzy + Uyy= = 0, (1) Uzz + yuyy <= 0.
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The characteristic roots are 35i2 The characteristic coordinates are xcost ysint and xsint ycost w... View the full answer
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