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  • Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 4 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 4 Maths Textbook Solution.

Answers (1)

Answer:

Proved  Adj\left ( A \right )= A

Hint:

Here, we use basic concept of adjoint of matrix.

Given:

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

Solution:

Here, let’s find cofactor

\begin{aligned} &C_{11}=+(0-4)=-4 \\ &C_{12}=-(-1)=1 \\ &C_{13}=+(4-0)=4 \\ &C_{21}=-(-3)=3 \\ &C_{22}=+(0)=0 \\ &C_{23}=-(-4)=4 \\ &C_{31}=+(-3-0)=-3 \\ &C_{32}=-(-1)=1 \\ &C_{33}=+(3)=3 \end{aligned}

So,

C_{i j}=\left[\begin{array}{ccc} -4 & 1 & 4 \\ 3 & 0 & 4 \\ -3 & 1 & 3 \end{array}\right]

Let’s find  Adj \left ( A \right )

Take the transpose of  C_{ij}

\operatorname{Adj}(A)=\left[\begin{array}{ccc} -4 & 3 & -3 \\ 1 & 0 & 1 \\ 4 & 4 & 3 \end{array}\right]

Hence we clearly see that Adj \left ( A \right )=A

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