# How do you know if a linear transformation is one-to-one or onto?

## How do you know if a linear transformation is one-to-one or onto?

If there is a pivot in each column of the matrix, then the columns of the matrix are linearly indepen- dent, hence the linear transformation is one-to-one; if there is a pivot in each row of the matrix, then the columns of A span the codomain Rm, hence the linear transformation is onto.

What is onto in linear algebra?

• A function y = f(x) is said to be onto (its codomain) if, for every y (in the codomain), there is an x such that y = f(x). Note: Every function is automatically onto its image by definition (Since we only talk about the range in calculus, this is probably why the codomain is never mentioned anymore).

### Is an exponential function one to one?

A function is one-to-one if and only if and only if. $f(x) = f(y) \\implies x = y$. This essentially captures the idea, only one input can produce a particular output, in a rigorous definition. Now for the simplest exponential function. $f(x) = e^x$.

What is the definition of one to one?

1. adjective [ADJECTIVE noun] In a one-to-one relationship, one person deals directly with only one other person. One-to-one is also an adverb. If there is a one-to-one match between two sets of things, each member of one set matches a member of the other set. directly; in person; person to person on an equal basis

## What is an example of one to one function?

A one-to-one function is a function in which the answers never repeat. A normal function can have two different input values that produce the same answer, but a one-to-one function does not. Examples of this are: f(x) = x + 2 because for every input, you will get a different output.

What is the matrix of a linear transformation?

The matrix of a linear transformation. The matrix of a linear transformation is a matrix for which \$$T(\\vec{x}) = A\\vec{x}\$$, for a vector \$$\\vec{x}\$$ in the domain of T. This means that applying the transformation T to a vector is the same as multiplying by this matrix.