Heergerneuu
2022-09-17
Answered

FInd the slope of the line perpendicular to $y=-\frac{14}{9}x+11$

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asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-02-25

Let $A\in {M}_{m\times n}\left(\mathbb{Q}\right)$ and $b\in {\mathbb{Q}}^{m}$ . Suppose that the system of linear equations Ax=b has a solution in $\mathbb{R}}^{n$ . Does it necessarily have a solution in $\mathbb{Q}}^{n$ ?

and I thought I'd give an interesting, possibly wrong, approach to solving it. I'm not sure if such things can be done, if not maybe you can help me refine.

I considered the form of the equality as

${A}^{\left(1\right)}{x}_{1}+\cdots +{A}^{\left(n\right)}{x}_{n}=b$

where$A}^{\left(i\right)$ is a column vector of A. I then noticed that for $x}_{i}\in \mathbb{R}\mathrm{\setminus}\mathbb{Q}=\mathbb{T$ then, and this is where I think I'm doing something forbidden, each x has the represenation

$x}_{1}={k}_{11}{\tau}_{1}+\cdots +{k}_{1p}{\tau}_{p$

$x}_{2}={k}_{21}{\tau}_{1}+\cdots +{k}_{2p}{\tau}_{p$

$\vdots$

$x}_{n}={k}_{n1}{\tau}_{1}+\cdots +{k}_{np}{\tau}_{p$ ,

where$\tau}_{i$ is a distinct irrational number, $k}_{ij}\in \mathbb{R$ , and p is the number of such distinct irrational numbers. I wound this out, but there may be a discrepancy with p and m. I feel this method can lead me to the answer, but I'm not sure where to go from here.

I end up getting something like this, I believe, after substitution:

$A({k}^{\left(1\right)}{\tau}_{1}+\cdots +{k}^{\left(p\right)}{\tau}_{p})=b$

Here,$k}^{\left(i\right)$ is the vector

$(({k}_{1i}),(\dots ),({k}_{ni}))$ .

I think there is no discrepancy with p and m because$A\in {M}_{m\times n}\left(\mathbb{Q}\right),K\in {M}_{n\times p}\left(\mathbb{R}\right)$ , and $\tau \in {M}_{p\times 1}\left(\mathbb{T}\right)$ , so

$(m\times n)\cdot (n\times p)\cdot (p\times 1)=m\times 1$ .

and I thought I'd give an interesting, possibly wrong, approach to solving it. I'm not sure if such things can be done, if not maybe you can help me refine.

I considered the form of the equality as

where

where

I end up getting something like this, I believe, after substitution:

Here,

I think there is no discrepancy with p and m because

asked 2021-03-04

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations.

$\{\begin{array}{c}x+y=0\\ 5x-2y-2z=12\\ 2x+4y+z=5\end{array}$

asked 2022-09-26

How do you use linear models to make pblackictions?

asked 2022-09-21

Find the slope of the line perpendicular to y=−3x−7

asked 2022-02-23

Suppose I have the linear equation

where

Is

Apparently the answer is no, but I am unable to find a counter-example. If anything, my reasoning (below) tells me W is a subspace.

1.

2.If

3. If

asked 2022-02-22

Problem: A metal plate whose temperature at the point (x,y) is given

Problem 1: Compute

Question 1:

Problem 2: Denote the position at time t by

Question 2: not sure how to proceed.