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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Your Input

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 $$$\left[\begin{array}{ccc}-2 & -13 & -10\\-6 & -12 & -6\\-4 & -5 & -2\end{array}\right]$$$.

Answer

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