Audrey Mckee
2022-09-12
Answered

Find the slope of the line perpendicular to 4x+2y=10

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asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-02-24

Consider a system of linear equations of the form

$\mathbf{A}\mathbf{x}=\mathbf{b},\mathbf{A}\in {\mathbb{R}}^{L\times K},\mathbf{x}\in {\mathbb{R}}^{L},\mathbf{b}\in {\mathbb{R}}^{K}$

with L variables$x}_{1},{x}_{2},\dots ,{x}_{L}\in \mathbb{R$ and $K\le L$ equations.

We are interested in finding a solution for a single variable x_l. Is there an explicit condition for existence of a unique solution for this variable?

Example: if${x}_{1}+2{x}_{2}+3{x}_{3}=3$ and $2{x}_{2}+3{x}_{3}=2$ , then there exist a unique solution ${x}_{1}=1$ for the variable $x}_{1$ , and we cannot find unique solutions for the other variables.

with L variables

We are interested in finding a solution for a single variable x_l. Is there an explicit condition for existence of a unique solution for this variable?

Example: if

asked 2022-09-23

Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the equation given (4, -5), 2x−5y=−10

asked 2022-05-21

I have a system of linear equations in the following form. How can I solve it in Matlab?

$\underset{a,b}{argmin}\sum _{i,j}[X(i,j)-a\times Y(i,j)-b{]}^{2}$

Where X and Y are known. I need to estimate a and b - which do not depend on (i,j).

$\underset{a,b}{argmin}\sum _{i,j}[X(i,j)-a\times Y(i,j)-b{]}^{2}$

Where X and Y are known. I need to estimate a and b - which do not depend on (i,j).

asked 2022-02-23

This is my first question here, so hopefully I will be able to explain my problem in a coherent way. My ultimate question is: do you see any way I can simplify the following system so I can have a more intuitive solution to it? Let me explain in details what I mean:

I want to characterize x,y,z that solve the following system of non-linear equations:

$\mathrm{\Delta}x=\frac{\theta \mathrm{\Delta}z\mathrm{\Delta}y}{\mathrm{\Delta}y-\theta \mathrm{\Delta}z}\text{}\text{}\text{}\text{}\text{}\text{(EQ1)}$

$\mathrm{\Delta}x+\mathrm{\Delta}y+\mathrm{\Delta}z=\stackrel{\u2015}{Y}\text{}\text{}\text{}\text{}\text{}\text{(EQ2)}$

$\theta {\left(\mathrm{\Delta}z\right)}^{2}+{\left(\mathrm{\Delta}y\right)}^{2}=\stackrel{\u2015}{U}\text{}\text{}\text{}\text{}\text{}\text{(EQ3)}$

where

$\mathrm{\Delta}x=x-\stackrel{\u2015}{x}$

$\mathrm{\Delta}y=y-\stackrel{\u2015}{y}$

$\mathrm{\Delta}z=z-\stackrel{\u2015}{z}$

and$0<\theta <1,\stackrel{\u2015}{Y},\stackrel{\u2015}{U},\stackrel{\u2015}{x},\stackrel{\u2015}{y}$ and $\stackrel{\u2015}{z}$ are parameters.

The way I've approached this was to parameterize (EQ2):

$\mathrm{\Delta}y+\mathrm{\Delta}z=\alpha$

such that$\alpha =\stackrel{\u2015}{Y}-\mathrm{\Delta}x$

For$\theta =0.8,\stackrel{\u2015}{x}=\stackrel{\u2015}{y}=\stackrel{\u2015}{z}=0.5$ and $\stackrel{\u2015}{Y}=-0.5$ and $\stackrel{\u2015}{U}=0.2$ this parametric system would look like the following (I apologize I don't have reputation to embed the photo here):

The parametric system

I can characterize$\mathrm{\Delta}y$ and $\mathrm{\Delta}z$ as a function of $\alpha$ :

$\mathrm{\Delta}y=\frac{\theta \alpha \pm \sqrt{\stackrel{\u2015}{U}(1+\theta )-\theta {\alpha}^{2}}}{1+\theta}$

$\mathrm{\Delta}z=\frac{\alpha \mp \sqrt{\stackrel{\u2015}{U}(1+\theta )-\theta {\alpha}^{2}}}{1+\theta}$

My problem arrives in the characterization of α using (EQ1). Although we can show such an$\alpha$ exists, it is far from an intuitive closed-form characterization, as $\alpha$ solves:

$\pm \frac{(\stackrel{\u2015}{Y}-\alpha )(1-\theta )\sqrt{\stackrel{\u2015}{U}(1+\theta )-\theta {\alpha}^{2}}}{\theta \alpha \pm \sqrt{\stackrel{\u2015}{U}(1+\theta )-\theta {\alpha}^{2}}}=\theta (\alpha \mp \sqrt{\stackrel{\u2015}{U}(1+\theta )-\theta {\alpha}^{2}})$

Am I using the correct approach to this problem? Or do you see anyway I could simplify this? Thank you!

I want to characterize x,y,z that solve the following system of non-linear equations:

where

and

The way I've approached this was to parameterize (EQ2):

such that

For

The parametric system

I can characterize

My problem arrives in the characterization of α using (EQ1). Although we can show such an

Am I using the correct approach to this problem? Or do you see anyway I could simplify this? Thank you!

asked 2022-02-22

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form. Solve the system.

asked 2022-09-22

The attendance at two baseball games on successive nights was 77,000. The attendance on Thursday's game was 7000 more than two-thirds of the attendance at Friday night's game. How many people attended the baseball game each night?