a11

a12

a13

a21

a23

a31

a32

a33

a11

a12

a13

a21

a22

a23

a31

a32

a33

a22

The Minor of the element 

=

a_2_2   a_2_3

a_3_2   a_3_3

a_2_1   a_2_3

a_3_1   a_3_3

a_2_1   a_2_2

a_3_1   a_3_2

a_1_2   a_1_3

a_3_2   a_3_3

a_1_1   a_1_3

a_3_1   a_3_3

a_1_1   a_1_2

a_3_1   a_3_2

a_1_2   a_1_3

a_2_2   a_2_3

a_1_1   a_1_3

a_2_1   a_2_3

a_1_1   a_1_2

a_2_1   a_2_2

The cofactor of the element

MINORS and COFACTORS

  A_i_j=(-1)^\left( {i +j }  \right) M_i_j

The cofactor of the element

a_i_j = 

by Benny Varghese
PGT Maths
JNV Pathanamthitta
Kerala-686511

Plz click a11 ,a12 etc

(

)

a: 1
b: 3
A: (a, b)
B: (a, 0)
C: (a, 4)
c = Segment(B, C)
D: (0, b)
E: (5, b)
d = Segment(D, E)
G = (0.5, 3.02)
H = (1.4, 3)
I = (0.98, 3.56)
e = Ellipse(G, H, I)
G_1 = (2.14, 3.02)
H_1 = (3.04, 3)
I_1 = (2.62, 3.56)
e_1 = Ellipse(G_1, H_1, I_1)
G_2 = (3.62, 2.98)
H_2 = (4.52, 2.96)
I_2 = (4.1, 3.52)
e_2 = Ellipse(G_2, H_2, I_2)
G_3 = (0.5, 1.98)
H_3 = (1.4, 1.96)
I_3 = (0.98, 2.52)
e_3 = Ellipse(G_3, H_3, I_3)
G_4 = (2.14, 1.96)
H_4 = (3.04, 1.94)
I_4 = (2.62, 2.5)
e_4 = Ellipse(G_4, H_4, I_4)
G_5 = (3.58, 1.9)
H_5 = (4.48, 1.88)
I_5 = (4.06, 2.44)
e_5 = Ellipse(G_5, H_5, I_5)
G_6 = (0.5, 0.88)
H_6 = (1.4, 0.86)
I_6 = (0.98, 1.42)
e_6 = Ellipse(G_6, H_6, I_6)
G_7 = (2.1, 0.86)
H_7 = (3, 0.84)
I_7 = (2.58, 1.4)
e_7 = Ellipse(G_7, H_7, I_7)
G_8 = (3.64, 0.88)
H_8 = (4.54, 0.86)
I_8 = (4.12, 1.42)
e_8 = Ellipse(G_8, H_8, I_8)
G_9: A
num2 = If(a ≟ 1, 1, If[a ≟ 2.5, 2, 3])
num1 = If(b ≟ 3, 1, If[b ≟ 2, 2, 3])
F = (14, 5)
J = (14.02, 2.52)
K = (17, 5)
L = (17.02, 2.5)
f = Segment(F, J)
g = Segment(K, L)
text2: "a_" + num1 + "_" + num2 + ""
A_1: (a, b)
B_1: (a, 0)
C_1: (a, 4)
D_1: (0, b)
E_1: (5, b)
num2_1 = If(a ≟ 1, 1, If[a ≟ 2.5, 2, 3])
num1_1 = If(b ≟ 3, 1, If[b ≟ 2, 2, 3])
text2_1: "a_" + num1_1 + "_" + num2_1 + ""
A_2: (a, b)
B_2: (a, 0)
C_2: (a, 4)
D_2: (0, b)
E_2: (5, b)
num2_2 = If(a ≟ 1, 1, If[a ≟ 2.5, 2, 3])
num1_2 = If(b ≟ 3, 1, If[b ≟ 2, 2, 3])
text5_2: "M_" + (LaTeX[num1_2]) + "_" + (LaTeX[num2_2]) + ""
text2_2: "a_" + num1_2 + "_" + num2_2 + ""
A_3: (a, b)
B_3: (a, 0)
C_3: (a, 4)
D_3: (0, b)
E_3: (5, b)
num2_3 = If(a ≟ 1, 1, If[a ≟ 2.5, 2, 3])
num1_3 = If(b ≟ 3, 1, If[b ≟ 2, 2, 3])
text2_3: "a_" + num1_3 + "_" + num2_3 + ""
A_4: (a, b)
B_4: (a, 0)
C_4: (a, 4)
D_4: (0, b)
E_4: (5, b)
num2_4 = If(a ≟ 1, 1, If[a ≟ 2.5, 2, 3])
num1_4 = If(b ≟ 3, 1, If[b ≟ 2, 2, 3])
text5_4: "M_" + (LaTeX[num1_4]) + "_" + (LaTeX[num2_4]) + ""
text2_4: "a_" + num1_4 + "_" + num2_4 + ""
text5: "A_" + (LaTeX[num1]) + "_" + (LaTeX[num2]) + ""
A_5: (a, b)
B_5: (a, 0)
C_5: (a, 4)
D_5: (0, b)
E_5: (5, b)
num2_5 = If(a ≟ 1, 1, If[a ≟ 2.5, 2, 3])
num1_5 = If(b ≟ 3, 1, If[b ≟ 2, 2, 3])
A_6: (a, b)
B_6: (a, 0)
C_6: (a, 4)
D_6: (0, b)
E_6: (5, b)
A_7: (a, b)
B_7: (a, 0)
C_7: (a, 4)
D_7: (0, b)
E_7: (5, b)
A_8: (a, b)
B_8: (a, 0)
C_8: (a, 4)
D_8: (0, b)
E_8: (5, b)
A_9: (a, b)
B_9: (a, 0)
C_9: (a, 4)
D_9: (0, b)
E_9: (5, b)
A_{10}: (a, b)
B_{10}: (a, 0)
C_{10}: (a, 4)
D_{10}: (0, b)
E_{10}: (5, b)
num2_6 = If(a ≟ 1, 1, If[a ≟ 2.5, 2, 3])
num1_6 = If(b ≟ 3, 1, If[b ≟ 2, 2, 3])
text2_6: "a_" + num1_6 + "_" + num2_6 + ""
A_{11}: (a, b)
B_{11}: (a, 0)
C_{11}: (a, 4)
D_{11}: (0, b)
E_{11}: (5, b)
A_{12}: (a, b)
B_{12}: (a, 0)
C_{12}: (a, 4)
D_{12}: (0, b)
E_{12}: (5, b)
A_{13}: (a, b)
B_{13}: (a, 0)
C_{13}: (a, 4)
D_{13}: (0, b)
E_{13}: (5, b)
A_{14}: (a, b)
B_{14}: (a, 0)
C_{14}: (a, 4)
D_{14}: (0, b)
E_{14}: (5, b)
a_1 = 1 (slider from 1 to 4, step 1)
b_1 = 3 (slider from 1 to 3, step 1)
A_{15}: (a_1, b_1)
B_{15}: (a_1, 0)
C_{15}: (a_1, 4)
D_{15}: (0, b_1)
E_{15}: (5, b_1)
num2_7 = If(a_1 ≟ 1, 1, If[a_1 ≟ 2.5, 2, 3])
num1_7 = If(b_1 ≟ 3, 1, If[b_1 ≟ 2, 2, 3])
text2_7: "a_" + num1_7 + "_" + num2_7 + ""
A_{16}: (a_1, b_1)
B_{16}: (a_1, 0)
C_{16}: (a_1, 4)
D_{16}: (0, b_1)
E_{16}: (5, b_1)
A_{17}: (a_1, b_1)
B_{17}: (a_1, 0)
C_{17}: (a_1, 4)
D_{17}: (0, b_1)
E_{17}: (5, b_1)
A_{18}: (a_1, b_1)
B_{18}: (a_1, 0)
C_{18}: (a_1, 4)
D_{18}: (0, b_1)
E_{18}: (5, b_1)
A_{19}: (a_1, b_1)
B_{19}: (a_1, 0)
C_{19}: (a_1, 4)
D_{19}: (0, b_1)
E_{19}: (5, b_1)
text7: "=(-1)^\left( {" + (LaTeX[num1]) + "+" + (LaTeX[num2]) + "}  \right) "
text2_5: "a_" + num1 + "_" + num2 + ""
F_1 = (-0.34, 3.28)