The linear equation is the equation that has a from: a_1x_1+a_2x_2+...+a_nx_n=b But



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The linear equation is the equation that has a from:
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?

Answer & Explanation

Miles Martin

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=(a1,,an) and x=(x1,,xn)T,
Andrew Fenton

Andrew Fenton

Beginner2022-02-18Added 6 answers

There are two different concepts here.
1) A linear equation such as a1x1+a2x2++anxn=b where the variables appear in the first degree.
2) A linear transformation which satisfies f(x+y)=f(x)+f(y)
For example 2x+3y=10 is a linear equation.
On the other hand f(x)=4x is a linear function or linear transformation.

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