Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

What is the determinant of a matrix used for?

1 Answer

Jun 1, 2015

The determinant of a matrix $A$ $A$ helps you to find the inverse matrix $A^{- 1}$ $A^(-1)$ .

You can know a few things with it :

$A$ $A$ is invertible if and only if $D e t (A) \neq 0$ $Det(A) != 0$ .
$D e t (A^{- 1}) = \frac{1}{D e t (A)}$ $Det(A^(-1)) = 1/(Det(A))$
$A^{- 1} = \frac{1}{D e t (A)} \cdot^{t} ({(- 1)}^{i + j} \cdot M_{i j})$ $A^(-1) = 1/(Det(A)) * ""^t((-1)^(i+j)*M_(ij))$ ,

where $t$ $t$ means the transpose matrix of $({(- 1)}^{i + j} \cdot M_{i j})$ $((-1)^(i+j)*M_(ij))$ ,

where $i$ $i$ is the n° of the line, $j$ $j$ is the n° of the column of $A$ $A$ ,

where ${(- 1)}^{i + j}$ $(-1)^(i+j)$ is the cofactor in the $i$ $i$ -th row and $j$ $j$ -th column of $A$ $A$ ,

and where $M_{i j}$ $M_(ij)$ is the minor in the $i$ $i$ -th row and $j$ $j$ -th column of $A$ $A$ .

Related questions

See all questions in Determinant of a Square Matrix

Impact of this question

4151 views around the world

You can reuse this answer
Creative Commons License