A = \(\left[ \begin{matrix} 8 & 2 \\ 4 & 3 \end{matrix} \right] \)
|A|=\(\left| \begin{matrix} 8 & 2 \\ 4 & 3 \end{matrix} \right| \)
= 24 – 8 = 16
≠ 0
∴ A என்ப து பூச்சியமற்ற கோவை அணி ஆகும்

B = \(\begin{vmatrix} 1 &-3 &2 \\4 &-1&2\\3&5&2 \end{vmatrix}\)
Minor of 1 = M₁₁ = \(\begin{vmatrix} -1 & 2 \\ 5 & 2 \end{vmatrix}=-2-10=-12\)
Minor of -3 = M₁₂ = \(\begin{vmatrix}4 &2 \\ 3 & 2 \end{vmatrix}=8-6=2\)
Minor of 2 = M₁₃ = \(\begin{vmatrix} 4 & -1 \\ 3 & 5\end{vmatrix}=20+3=23\)
Minor of 4 = M₂₁ = \(\begin{vmatrix} -3 & 2 \\5 & 2 \end{vmatrix}=-6+10=-16\)
Minor of -1 = M₂₂ = \(\begin{vmatrix}1 & 2 \\ 3 & 2 \end{vmatrix}=2-6=-4\)
Minor of 2 = M₂₃ = \(\begin{vmatrix} 1& -3 \\3 &5 \end{vmatrix}=5+9=14\)
Minor of 3 = M₃₁ = \(\begin{vmatrix} -3 &2 \\ -1 & 2 \end{vmatrix}=-6+2=-4\)
Minor of 3 = M₃₂ = \(\left|\begin{array}{ll} 1 & 2 \\ 4 & 2 \end{array}\right|=2-8=-6\)
Minor of 2 = M₃₃ = \(\begin{vmatrix} 1 & -3 \\4 & -1 \end{vmatrix}=-1+12=11\)
Co-factor of 1 = A₁₁ = (-1)¹⁺¹ M₁₁ = -12
Co-factor of -3 = A₁₂= (-1)¹⁺² M₁₂ = -2
Co-factor of 2 = A₁₃= (-1)¹⁺³ M₁₃ = 23
Co-factor of 4 = A₂₁ = (-1)²⁺¹ M₂₁ = 16
Co-factor of -1 = A₂₂ = (-1)²⁺² M₂₂ = -4
Co-factor of 2 = A₂₃ = (-1)2+3 M₂₃ = -14
Co-factor of 3 = A₃₁ = (-1)³⁺¹ M₃₁ = -4
Co- factor of 5 = A₃₂ = (-1)³⁺² M₃₂ = 6
Co-factor of 2 = A₃₃ = (-1)³⁺³ M₃₃ = 11

A = \(\left| \begin{matrix} 5 & 20 \\ 0 & -1 \end{matrix} \right| \)
Minor of 5 = M₁₁ = -1
Minor of 20 = M₁₂ = 0
Minor of 0 = M₂₁ = 20
Minor of -1 = M₂₂ = 5
Co-factor of 5 = A₁₁ = -1
Co-factor of 20 = A₁₂ = 0
Co-factor of 0 = A₂₁ = -20
Co-factor of -1 = A₂₂ = 5

\(\left| \begin{matrix} x & x+1 \\ x-1 & x \end{matrix} \right| \)= x²-(x – 1)(x + 1)
= x² – (x² – 1)
= x² – x² + 1 = 1

\(\left| \begin{matrix} 2 & 4 \\ -1 & 4 \end{matrix} \right| \) = (2)(4)-(-1)4
= 8 + 4 = 12

\(B=\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}\)
I - B =\(\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}=\begin{bmatrix} 0.50 & -0.25 \\ -0.40 & 0.33 \end{bmatrix}\)
\(|\mathrm{I}-\mathrm{B}|\) = 0.165 - 0.1 = 0.065 > 0
ஹாக்கின்ஸ் – சைமன் நிபந்தனைகளின்படி சாத்தியமானது

\(|A|=\left| \begin{matrix} -2 & 6 \\ 3 & -9 \end{matrix} \right| =0\)
A என்பது பூச்சிய கோவை அணி. எனவே A^-1 -யைக் காணஇயலாது

∴ |AB| = - 30

\(\left| \begin{matrix} 2 & x & 3 \\ 4 & 1 & 6 \\ 1 & 2 & 7 \end{matrix} \right| =0\)

⇒ 2 (7 -12) -x (28- 6) + 3 (8 - 1) = 0
⇒ -10 - 22x + 21 = 0
⇒ 11 = 22x
⇒ \(x={11\over 22}={1\over 2}\)

\(a_{ 11 }=15,\quad { a }_{ 12 }=10,\quad { x }_{ 1 }=35\)
\(a_{ 21 }=20,\quad { a }_{ 22 }=30,\quad { x }_{ 2 }=65\)
\(b_{ 11 }=\frac { { a }_{ 11 } }{ { x }_{ 1 } } =\frac { 15 }{ 35 } =\frac { 3 }{ 7 } ;\quad b_{ 12 }=\frac { { a }_{ 12 } }{ { x }_{ 2 } } =\frac { 10 }{ 65 } =\frac { 2 }{ 13 } \)
\(b_{ 21 }=\frac { { a }_{ 21 } }{ { x }_{ 1 } } =\frac { 20 }{ 35 } =\frac { 4 }{ 7 } ;\quad b_{ 22 }=\frac { { a }_{ 12 } }{ { x }_{ 2 } } =\frac { 30 }{ 65 } =\frac { 6 }{ 13 } \)
B = \(\begin{bmatrix} \frac { 3 }{ 7 } & \frac { 2 }{ 13 } \\ \frac { 4 }{ 7 } & \frac { 6 }{ 13 } \end{bmatrix}\)
\(I-B=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix} \frac { 3 }{ 7 } & \frac { 2 }{ 13 } \\ \frac { 4 }{ 7 } & \frac { 6 }{ 13 } \end{bmatrix}=\begin{bmatrix} \frac { 4 }{ 7 } & \frac { -2 }{ 13 } \\ \frac { 4 }{ 7 } & \frac { 7 }{ 13 } \end{bmatrix}\)
\(|I-B|=\frac{4}{7} \times \frac{7}{13}-\left(\frac{2}{13} \times \frac{4}{7}\right)=\frac{28-8}{91}=\frac{20}{91}\)
ஹாக்கின்ஸ்-சைமனின் இரு நிபந்தனைகளும் நிறைவு செய்யப்பட்டுள்ளது. எனவே இந்த பொருளாதாரக் கட்டமைப்பு செயல்படும் வகையில் உள்ளது.
 \((I-B)^{-1}=\frac{1}{|I-B|} \operatorname{adj}(\mathrm{I}-\mathrm{B})=\frac{91}{20}\left(\begin{array}{cc} \frac{7}{13} & \frac{2}{13} \\ \frac{4}{7} & \frac{4}{7} \end{array}\right)\)
X = (I - B)^-1 D இங்கு D \(=\left[ \begin{matrix} 12 \\ 18 \end{matrix} \right] =\frac { 91 }{ 20 } \begin{bmatrix} \frac { 7 }{ 13 } & \frac { 2 }{ 13 } \\ \frac { 4 }{ 7 } & \frac { 4 }{ 7 } \end{bmatrix}\left[ \begin{matrix} 12 \\ 18 \end{matrix} \right]=\frac{91}{20}\left(\begin{array}{l} \frac{84+36}{13} \\ \frac{48+72}{7} \end{array}\right)\)
\(=\left(\begin{array}{l} 42 \\ 78 \end{array}\right)\)
42 மற்றும் 78