Recall that the determinant of a 3-by-3 matrix is a b C de f gh i...

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Recall that the determinant of a 3-by-3 matrix is a b C de f gh i (a) If a, b, c, d, e, f, g, h, i are differentiable functions of the same variable, show that a' b' c d e 9 h 2 a b C de f 9 h 2 Ա u' u" = = aei- afh- bdi + bfg+cdh - ceg. a b C f+d' e' f' + d 9 h i a b = C f (b) Suppose u, v, and w satisfy the equation y"" V W v' w. Using the above, or otherwise, show that x' = px. V" W" e g' h'i' . py" + qy' + ry and let x = Recall that the determinant of a 3-by-3 matrix is a b C de f gh i (a) If a, b, c, d, e, f, g, h, i are differentiable functions of the same variable, show that a' b' c d e 9 h 2 a b C de f 9 h 2 Ա u' u" = = aei- afh- bdi + bfg+cdh - ceg. a b C f+d' e' f' + d 9 h i a b = C f (b) Suppose u, v, and w satisfy the equation y"" V W v' w. Using the above, or otherwise, show that x' = px. V" W" e g' h'i' . py" + qy' + ry and let x =