$\{\begin{array}{c}x-\mathrm{arctan}y=y-\mathrm{arctan}x\\ {x}^{2}-xy+4{y}^{2}=4\end{array}$

Rapsinincke
2022-07-01
Answered

$\{\begin{array}{c}x-\mathrm{arctan}y=y-\mathrm{arctan}x\\ {x}^{2}-xy+4{y}^{2}=4\end{array}$

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Camron Herrera

Answered 2022-07-02
Author has **16** answers

Without loss of generality we may suppose that $x\ge y$. But if $x>y$, what is the sign of $(\mathrm{arctan}y-\mathrm{arctan}x)$? conclude that $x=y$ and finish the job.

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Solve for j and k: $\{\begin{array}{l}2j+3k=-5\\ 6j+3k=2\end{array}$

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Let's say we have the general solution to ${X}^{\prime}=A(t)X$, where $X=({x}_{1},{x}_{2}{)}^{T}$. How do you find the general solution to the system ${X}^{\prime}=A(t)X+b(t)$ where $b(t)$ is a $2\times 1$ matrix with two polynomials as entries. How do you find the particular solution?

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Real world situation with System of Equation with 3 variables?

asked 2022-07-04

How to frame this set of linear equations?

$2x+1y+2z=A$

$0x+2y+2z=A$

$1x+2y+1z=A$

I assume this can be rewritten as a matrix? How can I check if a solution exists such that x, y, and z are nonnegative?

$2x+1y+2z=A$

$0x+2y+2z=A$

$1x+2y+1z=A$

I assume this can be rewritten as a matrix? How can I check if a solution exists such that x, y, and z are nonnegative?

asked 2022-09-10

Method to solve the following system of nonlinear equations?

$141,3829=A+\frac{B}{323}+5,78C+F{323}^{E}\phantom{\rule{0ex}{0ex}}69,07645=A+\frac{B}{333}+5,81C+F{333}^{E}\phantom{\rule{0ex}{0ex}}40,55085=A+\frac{B}{343}+5,84C+F{343}^{E}\phantom{\rule{0ex}{0ex}}27,92544=A+\frac{B}{353}+5,87C+F{353}^{E}\phantom{\rule{0ex}{0ex}}19,7697=A+\frac{B}{363}+5,89C+F{363}^{E}$

where $A,B,C,E,F$ are needs to be determined

$141,3829=A+\frac{B}{323}+5,78C+F{323}^{E}\phantom{\rule{0ex}{0ex}}69,07645=A+\frac{B}{333}+5,81C+F{333}^{E}\phantom{\rule{0ex}{0ex}}40,55085=A+\frac{B}{343}+5,84C+F{343}^{E}\phantom{\rule{0ex}{0ex}}27,92544=A+\frac{B}{353}+5,87C+F{353}^{E}\phantom{\rule{0ex}{0ex}}19,7697=A+\frac{B}{363}+5,89C+F{363}^{E}$

where $A,B,C,E,F$ are needs to be determined

asked 2022-05-27

system of linear equations:

$\{\begin{array}{l}(1+b)x+y+z=1\\ x+(1+b)y+z=b\\ x+y+(1+b)z={b}^{2}\end{array}$

And I would like to know if it has zero, one, or more solutions depanding on $b$ ($b\in \mathbb{R}$).

How do I do that?

$\{\begin{array}{l}(1+b)x+y+z=1\\ x+(1+b)y+z=b\\ x+y+(1+b)z={b}^{2}\end{array}$

And I would like to know if it has zero, one, or more solutions depanding on $b$ ($b\in \mathbb{R}$).

How do I do that?

asked 2022-05-16

How to determine the rank of a linear system of equations involving parameters?

For instance, the following matrix:

$\left(\begin{array}{ccc}k& 1& 1\\ 1& k& 1\\ 1& 1& k\end{array}\right)$

For instance, the following matrix:

$\left(\begin{array}{ccc}k& 1& 1\\ 1& k& 1\\ 1& 1& k\end{array}\right)$