Question

$\begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix}$

Answer 1

Given :     $A = \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix}$

To Find :  A⁻¹

Solution:

A⁻¹  =  AdjA / | A |

$A = \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix}$

| A |  = 1( 8 - 6) - (-1)( 0 - (-9) ) + 2(0 - 6)

=> | A | = 2 +9 - 12

=> | A | = -1

$Adj A = \begin{bmatrix} A_{11} & A_{21} & A_{31} \\ A_{12} & A_{22} & A_{32} \\ A_{13} & A_{23} & A_{33} \end{bmatrix}$

A₁₁  = (-1)¹⁺¹ ((2)*(4) - (-2)*(-3)) = 2

A₁₂ =  (-1)¹⁺² (0*(4) - (3)*(-3)) = -9

A₁₃ = (-1)¹⁺³(0*(-2) - (3)*(2)) = -6

A₂₁  = (-1)²⁺¹ ((-1)*(4) - (-2)*(2)) = 0

A₂₂ =  (-1)²⁺² (1*(4) - (3)*(2)) = -2

A₂₃ = (-1)²⁺³(1*(-2) - (3)*(-1)) = -1

A₃₁  = (-1)³⁺¹ ((-1)*(-3) - (2)*(2)) = -1

A₃₂ =  (-1)³⁺² (1*(-3) - (0)*(2)) = 3

A₃₃ = (-1)³⁺³(1*(2) - 0*(-1)) = 2

$AdjA = \begin{bmatrix} 2 & 0 & -1 \\ -9 & -2 & 3 \\ -6 & -1 & 2 \end{bmatrix}$      

A⁻¹  =

    $- \begin{bmatrix} 2 & 0 & -1 \\ -9 & -2 & 3 \\ -6 & -1 & 2 \end{bmatrix} \\ \\\\= \begin{bmatrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{bmatrix}$

और सीखें

निम्नलिखित सारणिकों के अवयवों के उपसारणिक एवं सहखण्ड ज्ञात कीजिए

brainly.in/question/16386652

दिए गए शीर्ष बिन्दुओं वाले त्रिभुजों का क्षेत्रफल ज्ञात कीजिए

brainly.in/question/16386350

A⁻¹

https://brainly.in/question/16386940

A⁻¹ ज्ञात कीजिए

https://brainly.in/question/16386935