Please I'm stuck with this review question, I tried to ask but you requested more information. Please answer all question and include a picture of your solution Let f (t) be the determinant of an n × n square matrix A (t) of differentiable functions5b.ajj (t), ¹ ≤ i, j ≤n. Show that the derivative of f is a sum of n determinants.IJustify the following steps(2 pts) Show that if f1, f2, ..., fn are differentiable functions on (a, b), thennd(ƒ₁ · ƒ2 · ... ·· · fn) (t) = Σ ƒ₁ (t) · f2 (t) · ... · fj−1 (t) · f' (t) · fj+1 (t) · ... · fndtj=1Use the following definition of the determinantto show thatf (t) = det A (t) = Σ sgn (0) a₁ 0(1) (t) · A2 0(2) (t) ).....an o(n) (t)σESnnf' (t) = sgn (o) Σ a1 o(1) (t) · .... · a(j−1) o(j−1) (t) · aj o(j) (t) · ª(j+1) o(j+1) (t) · · ... · an o(n) (t)σESnj=1 Argue thatnf'(t) = Σ Σ αισ(1) (t) ·) · .... · ª(j−1) o(j−1) (t) · a'j o(j) (t) · a(j+1) o(j+1) (t) ·j=10€ Sn• Let A; (t) be the matrix obtained from A (t) by differentiating the functions in the ith row of A (t)Show thatΣ sgn (0) a₁ 6(1) (t) · .σESnArgue that..... an o(n) (t)) · .... • α(j−1) o(j−1) (t) · aj o(j) (t) · a(j+1) o(j+1) (t) ·· · ... · an o(n) (t) = det A,nf' (t) = det Ajj=1

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5b. Let f(t) be the determinant of an n x n square matrix A (t) of differentiable functions a¡j (t), ¹ ≤ i, j ≤ n. Show that the derivative of f is a sum of n determinants. Justify the following steps (2 pts) Show that if f1, f2, ..., fn are differentiable functions on (a, b), then n d (f₁ · ƒ2 · ... · · fn) (t) = Σ ƒ1 (t) · ƒ2 (t) · ... · fj‒1 (t) · ƒ'; (t) · ƒj+1 (t) · ... · fn dt j=1

5b. Let f(t) be the determinant of an n x n square matrix A (t) of differentiable functions a¡j (t), ¹ ≤ i, j ≤ n. Show that the derivative of f is a sum of n determinants. Justify the following steps (2 pts) Show that if f1, f2, ..., fn are differentiable functions on (a, b), then n d (f₁ · ƒ2 · ... · · fn) (t) = Σ ƒ1 (t) · ƒ2 (t) · ... · fj‒1 (t) · ƒ'; (t) · ƒj+1 (t) · ... · fn dt j=1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 44E

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