Difference between revisions of "Inverse matrix"
Jump to navigation
Jump to search
m (Reverted edits by ThomasGrant (talk) to last revision by MatthewQ) |
DavidB4-bot (talk | contribs) (→top: Category) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | An '''inverse matrix''', or inverse of a [[matrix]], is the square matrix that produces the [[identity matrix]] when multiplied by its corresponding inverse. For a given matrix <math>A</math> the inverse exists if and only if the [[determinant]] of <math>A</math> is non-zero, <math>\det A \neq 0</math>. The inverse of an inverse is the original matrix. | + | An '''inverse matrix''', or [[inverse]] of a [[matrix]], is the square matrix that produces the [[identity matrix]] when multiplied by its corresponding inverse. For a given matrix <math>A</math> the inverse exists if and only if the [[determinant]] of <math>A</math> is non-zero, <math>\det A \neq 0</math>. The inverse of an inverse is the original matrix. |
The formula for finding the inverse of a 2x2 matrix is as follows: | The formula for finding the inverse of a 2x2 matrix is as follows: | ||
| Line 6: | Line 6: | ||
| − | [[Category: | + | [[Category:Linear Algebra]] |
Latest revision as of 14:35, July 28, 2016
An inverse matrix, or inverse of a matrix, is the square matrix that produces the identity matrix when multiplied by its corresponding inverse. For a given matrix <math>A</math> the inverse exists if and only if the determinant of <math>A</math> is non-zero, <math>\det A \neq 0</math>. The inverse of an inverse is the original matrix.
The formula for finding the inverse of a 2x2 matrix is as follows:
<math>A = \begin{pmatrix}a & b \\ c & d\end{pmatrix} \Rightarrow A^{-1} = \frac{1}{ad - bc}\begin{pmatrix} d & -b \\ -c & a\end{pmatrix} </math>.