Find the augmented matrix for the following system of linear equations:

Kyran Hudson
2021-03-05
Answered

Find the augmented matrix for the following system of linear equations:

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pivonie8

Answered 2021-03-06
Author has **91** answers

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asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2021-08-11

Determine the equation of the line in slope-intercept form which passes through the point (6. 6) and has the slope $-\frac{1}{3}$ . Simplify the answer, please.

asked 2022-02-24

Let X be a smooth hypersurface in Projective space $\mathbb{P}}^{n$ of degree d defined by the equation f=0. Given that we have a vector bundle E of rank $r\ge 1$ on X such that we have the following exact sequence on $\mathbb{P}}^{n$ :

$0\to O{(-1)}^{rd}\to {O}^{rd}\to E\to 0$ .

My question is as follows. What is the morphism from$O{(-1)}^{rd}\to {O}^{rd}$ ? A paper indicated that it is given by a $rd\times rd$ matrix of linear forms. Why is this? I am not able to see it. If this is so, can we say where in $\mathbb{P}}^{n$ the determinant of that matrix vanishes?

My question is as follows. What is the morphism from

asked 2022-02-24

I have no idea how to solve it. Should be linear equation of order one since I am passing through this chapter, but I can't put into the form of

${y}^{\prime}+P\left(x\right)y=Q\left(x\right)$

Here is the equation:

$(2xy+{x}^{2}+{x}^{4})dx-(1+{x}^{2})dy=0$

It is not exact since partial derivatives are not equal.

Any help would be appreciated.

Here is the equation:

It is not exact since partial derivatives are not equal.

Any help would be appreciated.

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 2021-02-21

Define Absolute system of Linear Equations?

asked 2022-02-24

During some computations I came up with the following system of linear recurrences:

$B}_{n+2}=3{B}_{n}+{A}_{n$

$A}_{n}={A}_{n-1}+{B}_{n-1$

Here I am trying to find the solution for B (hoping to get some sort of homogeneous equation, find it roots and get the closed form formula).

But I can't solve it. The only thing I can do is

$B}_{n+2}=3{B}_{n}+\sum _{i=0}^{n-1}{B}_{i$ ,

which will not help me to solve recurrence. So is there a way I can find B without the summation through n?

Here I am trying to find the solution for B (hoping to get some sort of homogeneous equation, find it roots and get the closed form formula).

But I can't solve it. The only thing I can do is

which will not help me to solve recurrence. So is there a way I can find B without the summation through n?