The reduced row echelon form of the augmented matrix of a system of three linear equations in three variables must be of the form

remolatg
2021-09-11
Answered

The reduced row echelon form of the augmented matrix of a system of three linear equations in three variables must be of the form

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Jozlyn

Answered 2021-09-12
Author has **85** answers

Reduced row echelon form consists of the first row starting off with a 1 followed by 0s

asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-02-25

Let $T:{\mathbb{R}}^{2}\to {\mathbb{R}}^{3}$ be the linear transformation defined by $T(x,y)=(y-x,-3x,-3y)$

Write a linear equation defining the subspace$Im\left(T\right)$

$\cdots =0Z$

(Write your answer in the form$ax+by+cz$ . For example "$2x+3y-4z$ ")

So, I somehow learned how to find the image or kernels, but have no idea how to write a linear equation of it. Can someone help me with it? At least please give me an answer to this question I can figure out how to do it.

Write a linear equation defining the subspace

(Write your answer in the form

So, I somehow learned how to find the image or kernels, but have no idea how to write a linear equation of it. Can someone help me with it? At least please give me an answer to this question I can figure out how to do it.

asked 2022-02-25

If we were given two points on a linear equation $({x}_{1},{y}_{1}),({x}_{2},{y}_{2})$ , it is quite easy to find the slope and use substitution to find the slope intercept form $y=mx+b$ , to graph it.

Is it possible to solve for b strictly in terms of$x}_{1},{y}_{1},{x}_{2},{y}_{2$ ?

Is it possible to solve for b strictly in terms of

asked 2022-02-15

In Linear Algebra Done Right, it defines the linear maps of a homogeneous system of linear equations with n variables and m equations as

$T({x}_{1},\dots ,{x}_{n})=(\sum _{k=1}^{n}{A}_{1,k}{x}_{k},\dots ,\sum _{k=1}^{n}{A}_{m,k}{x}_{k})=0$

My question is why the homogeneous system of linear equations can be expressed as the linear maps from$\mathbb{F}}^{n}\mapsto {\mathbb{F}}^{m$

My question is why the homogeneous system of linear equations can be expressed as the linear maps from

asked 2022-05-20

Given $m=385$, I have a linear equation system over a field ${\mathbb{F}}_{p}$ with $p$ a small prime (could be 5,7,11, something like this) with the following properties:

1.There are ${m}^{2}$ variables.

2. Every variable appears in exactly 7 equation.

3. Every equation contains at most 3 variables.

4. The coefficient of the variables is always 1.

5.The free term in the equations are always 0, with one specific equation (an equation of the form $3x=1$ for a specific variable $x$).

I am currently using SAGE. It solved nicely smaller equation systems, but this one killed it, even when constructing the matrix as sparse ("Error allocating matrix"). The question is - should I simply try a better (and less convenient) sparse matrix handling package, or is there a better way to deal with such sparse systems of equations? (I can do a little programming myself if needed).

1.There are ${m}^{2}$ variables.

2. Every variable appears in exactly 7 equation.

3. Every equation contains at most 3 variables.

4. The coefficient of the variables is always 1.

5.The free term in the equations are always 0, with one specific equation (an equation of the form $3x=1$ for a specific variable $x$).

I am currently using SAGE. It solved nicely smaller equation systems, but this one killed it, even when constructing the matrix as sparse ("Error allocating matrix"). The question is - should I simply try a better (and less convenient) sparse matrix handling package, or is there a better way to deal with such sparse systems of equations? (I can do a little programming myself if needed).

asked 2022-05-24

The standard form of a linear firs-order DE is

$\frac{dy}{dx}+P(x)y=Q(x)$

I think the equation is separable if and only if $P(x)$ and $Q(x)$ are constants, but I'm not sure. (Haven't found any counterexamples but also can't seem to prove it.) Can anyone confirm or deny that this is correct?

$\frac{dy}{dx}+P(x)y=Q(x)$

I think the equation is separable if and only if $P(x)$ and $Q(x)$ are constants, but I'm not sure. (Haven't found any counterexamples but also can't seem to prove it.) Can anyone confirm or deny that this is correct?

asked 2022-02-24

Why is the equation $\frac{dy}{dx}+P\left(x\right)y=Q\left(x\right)$ said to be standard form?

Well, I know that in linear differential equation the variable and its derivatives are raised to power of 1 or 0. But I am confused where did the standard form of linear differential equation came form?

That is, why is the equation$\frac{dy}{dx}+P\left(x\right)y=Q\left(x\right)$ said to be standard form?

Well, I know that in linear differential equation the variable and its derivatives are raised to power of 1 or 0. But I am confused where did the standard form of linear differential equation came form?

That is, why is the equation