Changes

===Example 1===

===Example 1===

Consider all the points (vectors) in the plane, ie, ''(x,y)'' acting under the transformation  

Consider all the points (vectors) in the plane, i.e., ''(x,y)'' acting under the transformation  

<math>\mathbf{A} = \begin{pmatrix}

<math>\mathbf{A} = \begin{pmatrix}

-6 & -2  \end{pmatrix}</math>.

-6 & -2  \end{pmatrix}</math>.

Now if we examine how this matrix acts on an arbitary point ''(a,b)'', we find that point is carried to

Now if we examine how this matrix acts on an arbitrary point ''(a,b)'', we find that point is carried to

<math>\mathbf{A} = \begin{pmatrix}3 & 1  \\-6 & -2  \end{pmatrix}\begin{pmatrix}a  \\b  \end{pmatrix} = \begin{pmatrix}3a+b  \\-6a-2b  \end{pmatrix} = \begin{pmatrix}1  \\-3  \end{pmatrix}(a+b)</math>,

<math>\mathbf{A} = \begin{pmatrix}3 & 1  \\-6 & -2  \end{pmatrix}\begin{pmatrix}a  \\b  \end{pmatrix} = \begin{pmatrix}3a+b  \\-6a-2b  \end{pmatrix} = \begin{pmatrix}1  \\-3  \end{pmatrix}(a+b)</math>,