If y - begin vmatrix f x - g x - h x cr18m-na-b- e n d v m a t r i x Then dy - dx is equal toA- beginvmatrix f-x - g-x - h-x c r18 m - n c ra-b-c e n d v m a t r i x B- Vbeginvmatrix 18 m - n c rf-x - g-x - h-x c ra-b-clend vmatrix C- beginvmatrix f - x - 18 a a crg-x - m - b rh - x - n - c e n d v m a t r i x D- Vbeginvmatrix 18 m - n c ra-b-clcrf-x - g-x - h-x e n d v m a t r i x

The correct option is A f'(x) amp; g'(x) amp;h'(x) 1 amp;m amp;n a amp;b amp;cy = f(x) amp; g(x) amp;h(x) 1 amp;m amp;n a amp;b am ...

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Byju's Answer

Standard XII

Mathematics

Transpose of a Matrix

If y ∼=∼ begi...

Question

If $y = ∣ ∣ ∣ ∣ \begin{matrix} f (x) & g (x) & h (x) 1 & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣$
Then $\frac{d y}{d x}$ is equal to

∣ ∣ ∣ ∣ \begin{matrix} f^{'} (x) & g^{'} (x) & h^{'} (x) 1 & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣

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∣ ∣ ∣ ∣ \begin{matrix} 1 & m & n f^{'} (x) & g^{'} (x) & h^{'} (x) a & b & c \end{matrix} ∣ ∣ ∣ ∣

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∣ ∣ ∣ ∣ ∣ \begin{matrix} f^{'} (x) & 1 & a g^{'} (x) & m & b h^{'} (x) & n & c \end{matrix} ∣ ∣ ∣ ∣ ∣

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∣ ∣ ∣ ∣ \begin{matrix} 1 & m & n a & b & c f^{'} (x) & g^{'} (x) & h^{'} (x) \end{matrix} ∣ ∣ ∣ ∣

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Solution

The correct option is A $∣ ∣ ∣ ∣ \begin{matrix} f^{'} (x) & g^{'} (x) & h^{'} (x) 1 & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣$
$y = ∣ ∣ ∣ ∣ \begin{matrix} f (x) & g (x) & h (x) 1 & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣ \Rightarrow \frac{d y}{d x} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{d f (x)}{d x} & \frac{d g (x)}{d x} & \frac{d h (x)}{d x} 1 & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣ ∣ \Rightarrow \frac{d y}{d x} = ∣ ∣ ∣ ∣ \begin{matrix} f^{'} (x) & g^{'} (x) & h^{'} (x) 1 & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣$

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Similar questions

$I f y = ∣ ∣ ∣ ∣ \begin{matrix} f (x) & g (x) & h (x) l & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣, p r o v e t h a t \frac{d y}{d x} = ∣ ∣ ∣ ∣ \begin{matrix} f^{'} (x) & g^{'} (x) & h^{'} (x) l & m & m a & b & c \end{matrix} ∣ ∣ ∣ ∣$

If $A = (\begin{matrix} - 6 & - 1 9 & 1 \end{matrix}) B = (\begin{matrix} 2 & 0 - 3 & 5 \end{matrix})$ and $C = (\begin{matrix} - 1 & 8 7 & - 7 \end{matrix})$
Find A-B+C

Which of the following would be the Inverse of the matrix A found using Elementary Row Transformations where

A = $∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 & 1 0 & 1 & 1 3 & 6 & 1 \end{matrix} ∣ ∣ ∣ ∣$

Based on Table 1, the balance on the current account is:

Table 1

$\begin{matrix} Exports of goods and services & 1000 Imports of goods and services & 800 Net change in assets owned abroad & 500 Net change in foreign owned assets at home & 400 Unilateral transfers received & 100 Unilateral transfers paid & 200 Investment income paid to foreigners & 300 Investment income received from foreigners & 400 \end{matrix}$

Inverse of thefollowing matrix using elementary Row transformations would be

$= ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 & 1 0 & 1 & 1 3 & 6 & 1 \end{matrix} ∣ ∣ ∣ ∣$

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If y = ∣∣ ∣∣f(x)g(x)h(x)1mnabc∣∣ ∣∣ Then dydx is equal to

The correct option is A ∣∣ ∣∣f′(x)g′(x)h′(x)1mnabc∣∣ ∣∣y = ∣∣ ∣∣f(x)g(x)h(x)1mnabc∣∣ ∣∣⇒dydx = ∣∣ ∣ ∣∣df(x)dxdg(x)dxdh(x)dx1mnabc∣∣ ∣ ∣∣⇒dydx = ∣∣ ∣∣f′(x)g′(x)h′(x)1mnabc∣∣ ∣∣

If $y = ∣ ∣ ∣ ∣ \begin{matrix} f (x) & g (x) & h (x) 1 & m & n a & b & c \end{matrix} ∣ ∣ ∣ ∣$
Then $\frac{d y}{d x}$ is equal to