Question

$\begin{bmatrix} 2 & 1 & 3 \\ 4 & -1 & 0 \\ -7 & 2 & 1 \end{bmatrix}$

Answer 1

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Answer 2

Given :  $A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & -1 & 0 \\ -7 & 2 & 1 \end{bmatrix}$

To Find :  A⁻¹

Solution:

A⁻¹  =  AdjA / | A |

$A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & -1 & 0 \\ -7 & 2 & 1 \end{bmatrix}$

| A |  = 2( - 1 - 0) - 1( 4 - 0) + 3(8 - 7)

=> | A | = -2 - 4 + 3

=> | A | = -3

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

A₁₁  = (-1)¹⁺¹ ((-1)*(1) - 2*(0)) = -1 

A₁₂ =  (-1)¹⁺² (4*(1) - (-7)*(0)) = -4

A₁₃ = (-1)¹⁺³(4*2 - (-7)*(-1)) = 1

A₂₁  = (-1)²⁺¹ (1*(1) - 2*(3)) = 5

A₂₂ =  (-1)²⁺² (2*(1) - (-7)*(3)) = 23

A₂₃ = (-1)²⁺³(2*2 - (-7)*(1)) = -11

A₃₁  = (-1)³⁺¹ (1*0 - (-1)*(3)) = 3

A₃₂ =  (-1)³⁺² (2*(0) - (4)*(3)) = 12

A₃₃ = (-1)³⁺³(2*(-1) - 4*(1)) = -6

$Adj A = \begin{bmatrix} -1 & 5 & 3 \\ -4 & 23 & 12 \\ 1 & -11 & -6 \end{bmatrix}$      

A⁻¹  =    $\frac{-1}{3} \begin{bmatrix} -1 & 5 & 3 \\ -4 & 23 & 12 \\ 1 & -11 & -6 \end{bmatrix}$

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