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Questions -
Q1. Let f(t), g(t) be two functions having derivatives of all orders. Let φ(t) be the function obtained by taking the determinant,
Show that
i.e., the derivative is obtained by taking the derivative of the bottom row.
Q2. Let
be a 2 x 2 matrix of differentiable functions. Let B(t) and C(t) be its column vectors. Let
φ(t) = Det (A(t))
show that
φ'(t) = D(B'(t), C(t)) + D(B(t), C'(t))
Textbook - LINEAR ALGEBRA, undergraduate texts in Mathematics, (3rd Edition) by Serge Lang.
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