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  • Provide Solution for RD Sharma Class 12 Chapter 6 Adjoint and Inverse Matrix Exercise 6.1 Question 37

Provide Solution for RD Sharma Class 12 Chapter 6 Adjoint and Inverse Matrix Exercise 6.1 Question 37

Answers (1)

Answer:

\left[\begin{array}{ccc} -9 & -8 & -2 \\ 8 & 7 & 2 \\ -5 & -4 & -1 \end{array}\right]

Hint:

Here, we use basic concept of determinant and inverse of matrix

A^{-1}=\frac{1}{|A|} \times \operatorname{Adj}(A)

Given:

A=\left[\begin{array}{ccc} 1 & -2 & 3 \\ 0 & -1 & 4 \\ -2 & 2 & 1 \end{array}\right]

Solution:

A^{T}=\left[\begin{array}{ccc} 1 & 0 & -2 \\ -2 & -1 & 2 \\ 3 & 4 & 1 \end{array}\right]

Let’s find  \left | A^{T} \right |

\begin{aligned} &\left|A^{T}\right|=(-1-8)-0-2(-8+3) \\ &=-9+10=1 \end{aligned}                                                  

Cofactor of A^{T}

\begin{aligned} &C_{11}=-9, C_{12}=8, C_{13}=-5 \\ &C_{21}=-8, C_{22}=7, C_{23}=-4 \\ &C_{31}=-2, C_{32}=2, C_{33}=1 \end{aligned}

\operatorname{Adj}\left(A^{T}\right)=\left[\begin{array}{ccc} -9 & -8 & -2 \\ 8 & 7 & 2 \\ -5 & -4 & -1 \end{array}\right]

\left(A^{T}\right)^{-1}=\frac{1}{1}\left[\begin{array}{ccc} -9 & -8 & -2 \\ 8 & 7 & 2 \\ -5 & -4 & -1 \end{array}\right]

\left(A^{T}\right)^{-1}=\left[\begin{array}{ccc} -9 & -8 & -2 \\ 8 & 7 & 2 \\ -5 & -4 & -1 \end{array}\right] 

 

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