ennuvolat4gv

2022-02-16

The linear equation is the equation that has a from:

${a}_{1}{x}_{1}+{a}_{2}{x}_{2}+\dots +{a}_{n}{x}_{n}=b$

But is this really the definition of a linear equation? I thought that the definition should be the form of linear mapping. Like,

$f(x+y)=f\left(x\right)+f\left(y\right)$

$f\left(ax\right)=af\left(x\right)$

What is the definition of a linear equation?

But is this really the definition of a linear equation? I thought that the definition should be the form of linear mapping. Like,

What is the definition of a linear equation?

Miles Martin

Beginner2022-02-17Added 6 answers

The second defines a linear function, not a linear equation. For a matrix A, the function f(x)=Ax is linear. For

$A=({a}_{1},\dots ,{a}_{n})$ and $x={({x}_{1},\dots ,{x}_{n})}^{T}$ ,

$Ax={a}_{1}{x}_{1}+{a}_{2}{x}_{2}+\dots +{a}_{n}{x}_{n}$

Andrew Fenton

Beginner2022-02-18Added 6 answers

There are two different concepts here.

1) A linear equation such as${a}_{1}{x}_{1}+{a}_{2}{x}_{2}+\dots +{a}_{n}{x}_{n}=b$ where the variables appear in the first degree.

2) A linear transformation which satisfies$f(x+y)=f\left(x\right)+f\left(y\right)$

$f\left(ax\right)=af\left(x\right)$

For example$2x+3y=10$ is a linear equation.

On the other hand$f\left(x\right)=4x$ is a linear function or linear transformation.

1) A linear equation such as

2) A linear transformation which satisfies

For example

On the other hand

Find the volume V of the described solid S

A cap of a sphere with radius r and height h.

V=??

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

?

$d)f\left(x\right)={x}^{5}+1$In how many different orders can five runners finish a race if no ties are allowed???

State which of the following are linear functions?

a.$f(x)=3$

b.$g(x)=5-2x$

c.$h\left(x\right)=\frac{2}{x}+3$

d.$t(x)=5(x-2)$ Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

A square is also a

A)Rhombus;

B)Parallelogram;

C)Kite;

D)none of theseWhat is the order of the numbers from least to greatest.

$A=1.5\times {10}^{3}$,

$B=1.4\times {10}^{-1}$,

$C=2\times {10}^{3}$,

$D=1.4\times {10}^{-2}$Write the numerical value of $1.75\times {10}^{-3}$

Solve for y. 2y - 3 = 9

A)5;

B)4;

C)6;

D)3How to graph $y=\frac{1}{2}x-1$?

How to graph $y=2x+1$ using a table?

simplify $\sqrt{257}$

How to find the vertex of the parabola by completing the square ${x}^{2}-6x+8=y$?

There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?

Write 18 thousand in scientific notation.