$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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A equation is nonhomogenous if $Ax=y$ where $y\neq 0$. It possible has no solutions, a unique solution, or infinite solutions.

Concepts

If we view the matrix $A$ as a linear transformation, then $Ax=y$ has a solution if and only if $y\in \text{Ran} A$
If we're soluving the system, then the three possible outcomes are $Ax=y$ where $y\neq 0$ has
  • no solution
  • one solution
  • infinite solutions

Used In

  • Nonhomogenous equations are often represetnted with an augmented matrix

Hypothesis

Coming soon

Results

Coming soon
A equation is nonhomogenous if $Ax=y$ where $y\neq 0$. It possible has no solutions, a unique solution, or infinite solutions.

Concepts

If we view the matrix $A$ as a linear transformation, then $Ax=y$ has a solution if and only if $y\in \text{Ran} A$
If we're soluving the system, then the three possible outcomes are $Ax=y$ where $y\neq 0$ has
  • no solution
  • one solution
  • infinite solutions

Used In

  • Nonhomogenous equations are often represetnted with an augmented matrix

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results
FullPage
definition
concepts
used in
hypothesis
results
A equation is nonhomogenous if $Ax=y$ where $y\neq 0$. It possible has no solutions, a unique solution, or infinite solutions.

Concepts

If we view the matrix $A$ as a linear transformation, then $Ax=y$ has a solution if and only if $y\in \text{Ran} A$
If we're soluving the system, then the three possible outcomes are $Ax=y$ where $y\neq 0$ has
  • no solution
  • one solution
  • infinite solutions

Used In

  • Nonhomogenous equations are often represetnted with an augmented matrix

Hypothesis

Coming soon

Results

Coming soon
A equation is nonhomogenous if $Ax=y$ where $y\neq 0$. It possible has no solutions, a unique solution, or infinite solutions.

Concepts

If we view the matrix $A$ as a linear transformation, then $Ax=y$ has a solution if and only if $y\in \text{Ran} A$
If we're soluving the system, then the three possible outcomes are $Ax=y$ where $y\neq 0$ has
  • no solution
  • one solution
  • infinite solutions

Used In

  • Nonhomogenous equations are often represetnted with an augmented matrix

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results