Difference between revisions of "Determinants MA265F11Walther" - Rhea

Revision as of 14:48, 7 December 2011

If A is a square matrix then the determinant function is denoted by det and det(A)

For an instance we have a 2 x 2 matrix denominated A, therefore:

det(A) = [a₁₁ , a₁₂ ; a₂₁ , a₂₂]

As we already defined the determinant function we can write some formulas. The formulas for any 2 x 2 and 3 x 3 matrix will be:

The determinant function for a 2 x 2 matrix is:

det(A) = [a₁₁ , a₁₂ ; a₂₁ , a₂₂]

= a₁₁ * a₂₂ - a₁₂ * a₂₁

<sub</sub> $<math>\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right)$ </math>

The determinant function for a 3 x 3 matrix is:

det(A) = [a₁₁ , a₁₂, a₁₃ ; a₂₁ , a₂₂ , a₂₃ ; a₃₁ , a₃₂ , a₃₃]

= (a₁₁ * a₂₂ * a₃₃) + (a₁₂ * a₂₃ * a₃₁) + (a₁₃ * a₂₁ * a₃₂) - (a₁₂ * a₂₁ * a₃₃) - (a₁₁ * a₂₃ * a₃₂) - (a₁₃ * a₂₂ * a₃₁)

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+<sub</sub><math><math>\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right)</math></math>&nbsp;
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-<math><math>\left(\begin{array}{cccc}1&2&3&4\\5&6&7&8\end{array}\right)</math></math><br>
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