19. IF A = 3x9²²¹ 2 + 2xy²j - x²yek & 8 = 3x² - y2 FIND: A) 7. À @ (1,-1,₁1) *- - - - = a d + + ax • A = 2(3x42²) + (2x4²³) + 2/₂² (-x²³ y ²) = 2 32 = ax dz oy 3 yz ² + b xy² - x²y @ (1,-1,1) 3(-1)(0)² + 6(1)(-0²-(0)² (-1) = -3 + 6 - (-1) = (4) dz B. F. (DA) @ (1,-1, 1) (px) = (3xyz^2 + 2x4²3 - x^4²6) (3x²-ye) - 3 3 (3x² - y²) (3 xyz²)i + (3x² - y2) (2x4³) ; - (3x² - y²) (x²y²) k = 9x³y²² - 3 xy² 2² 2 + 6x³y² - 2xy^2; ; - 3x^y² - x^²y^² 2²¹ 7 7. (DA) = 2(9x³y2²-3x4³2³)+2 (6x³y² - 2xy^2); + (-3x^yz -x²y²2²) × = d dz dy 27x²92²- 34²2²2 - 27 x²y' - sxy³2) + (-3x^4 -2x³y²z) k 27 (1) ² (-1) (1)²-3 (-1)² (1) ³ + 27 (1) ³ (-1)² - 8 (1) (-1) ³ (1) + (-3 (1) + (-1) - 2 (1)²2-17² (1)
19. IF A = 3x9²²¹ 2 + 2xy²j - x²yek & 8 = 3x² - y2 FIND: A) 7. À @ (1,-1,₁1) *- - - - = a d + + ax • A = 2(3x42²) + (2x4²³) + 2/₂² (-x²³ y ²) = 2 32 = ax dz oy 3 yz ² + b xy² - x²y @ (1,-1,1) 3(-1)(0)² + 6(1)(-0²-(0)² (-1) = -3 + 6 - (-1) = (4) dz B. F. (DA) @ (1,-1, 1) (px) = (3xyz^2 + 2x4²3 - x^4²6) (3x²-ye) - 3 3 (3x² - y²) (3 xyz²)i + (3x² - y2) (2x4³) ; - (3x² - y²) (x²y²) k = 9x³y²² - 3 xy² 2² 2 + 6x³y² - 2xy^2; ; - 3x^y² - x^²y^² 2²¹ 7 7. (DA) = 2(9x³y2²-3x4³2³)+2 (6x³y² - 2xy^2); + (-3x^yz -x²y²2²) × = d dz dy 27x²92²- 34²2²2 - 27 x²y' - sxy³2) + (-3x^4 -2x³y²z) k 27 (1) ² (-1) (1)²-3 (-1)² (1) ³ + 27 (1) ³ (-1)² - 8 (1) (-1) ³ (1) + (-3 (1) + (-1) - 2 (1)²2-17² (1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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