Solutions > Matrix Minors & Cofactors Calculator >

Matrix Minors & Cofactors Calculator

Full pad

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

diagonalize eigenvalues eigenvectors gauss jordan unit

See All

area

asymptotes

critical points

derivative

domain

eigenvalues

eigenvectors

expand

extreme points

factor

implicit derivative

inflection points

intercepts

inverse

laplace

inverse laplace

partial fractions

range

slope

simplify

solve for

tangent

taylor

vertex

geometric test

alternating test

telescoping test

pseries test

root test

Steps Examples

Generated by AI

cofactors (

1	2	1
6	−1	0
−1	−2	−1

)

Solution

(

1	6	−13
0	0	0
1	6	−13

)

Show Steps

Hide Steps

Solution steps

One step at a time

(

1	2	1
6	−1	0
−1	−2	−1

)

Matrix minors and cofactors

A minor M_{i, j} is the determinant of the square matrix formed by deleting row i and column j from larger square matrix A.
A cofactor C_{i, j} is minor M_{i, j} when i+j is even and −M_{i, j} when i+j is odd thus C_{i, j}=(−1)^i+jM_{i, j}

M_{1, 1}=det(

−1	0
−2	−1

): 1

M_{1, 2}=det(

6	0
−1	−1

): −6

M_{1, 3}=det(

6	−1
−1	−2

): −13

M_{2, 1}=det(

2	1
−2	−1

): 0

M_{2, 2}=det(

1	1
−1	−1

): 0

M_{2, 3}=det(

1	2
−1	−2

): 0

M_{3, 1}=det(

2	1
−1	0

): 1

M_{3, 2}=det(

1	1
6	0

): −6

M_{3, 3}=det(

1	2
6	−1

): −13

Matrix of Minors M_{i, j}

(

1	−6	−13
0	0	0
1	−6	−13

)

Matrix of Cofactors C_{i, j}=(−1)^i+jM_{i, j}

(

(−1)⁰⁺⁰· 1	(−1)⁰⁺¹(−6)	(−1)⁰⁺²(−13)
(−1)¹⁺⁰· 0	(−1)¹⁺¹· 0	(−1)¹⁺²· 0
(−1)²⁺⁰· 1	(−1)²⁺¹(−6)	(−1)²⁺²(−13)