Matrix of Minors Calculator

The calculator will find the matrix of minors of the given square matrix, with steps shown.

Related calculator: Cofactor Matrix Calculator

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Find the matrix of minors of $\left[\begin{array}{ccc}1 & 2 & 3\\4 & 6 & 7\\7 & 8 & 9\end{array}\right]$.

Solution

The matrix of minors consists of all minors of the given matrix.

Minor $M_{ij}$ is the determinant of the submatrix formed by deleting row $i$ and column $j$ from the given matrix.

Calculate all minors:

$M_{11} = \left|\begin{array}{cc}6 & 7\\8 & 9\end{array}\right| = -2$ (for steps, see determinant calculator).

$M_{12} = \left|\begin{array}{cc}4 & 7\\7 & 9\end{array}\right| = -13$ (for steps, see determinant calculator).

$M_{13} = \left|\begin{array}{cc}4 & 6\\7 & 8\end{array}\right| = -10$ (for steps, see determinant calculator).

$M_{21} = \left|\begin{array}{cc}2 & 3\\8 & 9\end{array}\right| = -6$ (for steps, see determinant calculator).

$M_{22} = \left|\begin{array}{cc}1 & 3\\7 & 9\end{array}\right| = -12$ (for steps, see determinant calculator).

$M_{23} = \left|\begin{array}{cc}1 & 2\\7 & 8\end{array}\right| = -6$ (for steps, see determinant calculator).

$M_{31} = \left|\begin{array}{cc}2 & 3\\6 & 7\end{array}\right| = -4$ (for steps, see determinant calculator).

$M_{32} = \left|\begin{array}{cc}1 & 3\\4 & 7\end{array}\right| = -5$ (for steps, see determinant calculator).

$M_{33} = \left|\begin{array}{cc}1 & 2\\4 & 6\end{array}\right| = -2$ (for steps, see determinant calculator).

Thus, the matrix of minors is $\left[\begin{array}{ccc}-2 & -13 & -10\\-6 & -12 & -6\\-4 & -5 & -2\end{array}\right]$.

The matrix of minors is $\left[\begin{array}{ccc}-2 & -13 & -10\\-6 & -12 & -6\\-4 & -5 & -2\end{array}\right]$A.