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  • Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 3 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 3 Maths Textbook Solution.

Answers (1)

Answer:

Proved  A(\operatorname{Adj}(A))=0

Hint:

Here, we have to use advance method of finding adjoint of matrix.

Given:

A=\left[\begin{array}{ccc} 1 & -1 & 1 \\ 2 & 3 & 0 \\ 18 & 2 & 10 \end{array}\right]      

Solution:

We know that,

A \times \operatorname{Adj}(A)=|A| I  Then,

\left | A \right |I= 0                       (1)

From the equation (1)

\left | A \right |I= 0

\left|\begin{array}{ccc} 1 & -1 & 1 \\ 2 & 3 & 0 \\ 18 & 2 & 10 \end{array}\right| \times 1=0                                                      since, |I| =1

1\left|\begin{array}{rr} 3 & 0 \\ 2 & 10 \end{array}\right|-(-1)\left|\begin{array}{cc} 2 & 0 \\ 18 & 10 \end{array}\right|+1\left|\begin{array}{cc} 2 & 3 \\ 18 & 2 \end{array}\right|=0

\begin{aligned} &0=1(30)+(20-0)+(4-54) \\ &0=30+20+4-54 \\ &0=54-54 \\ &0=0 \end{aligned}

So, A \times \operatorname{Adj}(A)=|A| I=0

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