In case you want to pretty-print your matrices, you can either use
[tt]...
[/tt] and Unicode characters (Bracket Pieces from the
Unicode Miscellaneous Technical set, U+239B to U+23AE:
⎡ 0.75 -0.50 0.0 ⎤ ⎡ a ⎤ ⎡ 7 ⎤ ⎢ -0.5 4/3 -1/3 ⎥ ⎢ b ⎥ = ⎢ -4 ⎥ ⎣ 0 -1/3 5/6 ⎦ ⎣ c ⎦ ⎣ 7 ⎦Or, you can use MathJax. Using
$$ \left [ \begin{matrix} 0.75 & -0.50 & 0.0 \\ -0.5 & 4/3 & -1/3 \\ 0 & -1/3 & 5/6 \\ \end{matrix} \right ] \left [ \begin{matrix} a \\ b \\ c \\ \end{matrix} \right ] = \left [ \begin{matrix} 7 \\ -4 \\ 7 \\ \end{matrix} \right ] $$you get $$ \left [ \begin{matrix}
0.75 & -0.50 & 0.0 \\
-0.5 & 4/3 & -1/3 \\
0 & -1/3 & 5/6 \\
\end{matrix} \right ] \left [ \begin{matrix}
a \\ b \\ c \\
\end{matrix} \right ] = \left [ \begin{matrix}
7 \\ -4 \\ 7 \\
\end{matrix} \right ]$$
but unfortunately it does not show up correctly in preview, only when you post. The
MathJax Quick Reference at StackOverflow works here too, except that inline math expressions must be
\$ ... \$ , a single $ does not suffice here. Again, preview does not show the rendered version, you'll only see the result when posting.
I do like to recommend
maxima (text-based) or
wxMaxima (GUI version), both available for all OSes (Windows, Macs, Linux, source code for others), and is free of cost and licensed under the GPL. The single-page manual can be found
here. With maxima:
A : matrix([ 3/4, -1/2, 0], [ -1/2, 4/3, -1/3 ], [ 0, -1/3, 5/6 ]) $ determinant(A);shows the determinant of the matrix, 13/24. To solve
A.x = y for column vector
x, we construct column vector
y,
y : matrix([ 7 ], [ -4 ], [ 7 ]) $and obtain the result via
x = (A^^-1) . y,
invert(A) . y;which shows the result,
x : matrix([ 12 ], [ 4 ], [10]) $.
(Maxima matrix functions are listed e.g.
here.)