Exploring Analyic Geometry with Mathematica®

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Determinants

deter.html

Exploration

Determinants often provide a concise notation for expressing relationships in analytic geometry.  Show that the expanded algebraic form for the 2×2 determinant

"deter_1.gif"

is given by "deter_2.gif".

Show that the expanded algebraic form for the 3×3 determinant

"deter_3.gif"

is given by "deter_4.gif".

Approach

Use the Mathematica Det command to compute the desired determinants.

Initialize

To initialize Descarta2D, select the input cell bracket and press SHIFT-Enter.

This initialization assumes that the Descarta2D software has been copied into one of the standard directories for AddOns which are on the Mathematica search path, $Path.

<<Descarta2D`

Solution

The Det command produces the desired results directly.

Clear[a1,b1,a2,b2];
Det[{{a1,b1},{a2,b2}}]

"deter_5.gif"

Clear[a1,b1,c1,a2,b2,c2,a3,b3,c3];
Det[{{a1,b1,c1},{a2,b2,c2},{a3,b3,c3}}]

"deter_6.gif"


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