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The-Inverse-of-a-Square-Matrix

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Saved by Justin
on December 16, 2008 at 7:09:22 pm
 

The Inverse of a Square Matrix

 

Invertible/Nonsingular Matrix - any matrix that has an inverse

 

Singular Matrix - any matrix that does not have an inverse; either a non-square matrix or a square matrix with a determinant of 0 (he

 

An invertible matrix multiplied by its inverse will produce the identity matrix, a square matrix that is indicated by I and has 1s along the diagonal from the top-left corner of the matrix to the bottom-right corner along with 0s in all other spots.

 

 I_1=\begin{bmatrix} 1 \end{bmatrix} , I_2=\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} , I_3=\begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} ,\ \cdots , I_n=\begin{bmatrix} 1 & 0 & \cdots & 0 \ 0 & 1 & \cdots & 0 \ \vdots & \vdots & \ddots & \vdots \ 0 & 0 & \cdots & 1 \end{bmatrix}

 

To show that two matrics are inverses, you should multiply them and produce the identity matrix.

 

A and B are inverses.

 

 

To find the inverse of a 2x2 matrix, use the following equation:     
 

where  is derived from the original matrix 

 

 

 

Click Here for a video that explains and works out some inverse matrices problems.

 

 

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