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  • Need solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and Inverse of Matrices Excercise 6.1 Question 7 Subquestion (iv)

Need solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and Inverse of Matrices Excercise 6.1 Question 7 Subquestion (iv)

Answers (1)

Answer:

A^{-1}=\frac{1}{17}\left[\begin{array}{cc} 1 & -5 \\ 3 & 2 \end{array}\right]

Hint:

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

Given:

A=\left[\begin{array}{cc} 2 & 5 \\ -3 & 1 \end{array}\right]   

Solution:

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

So let’s find  \left | A \right |

|A|=\left|\begin{array}{ll} 2 & 5 \\ -3 & 1 \end{array}\right|=2-[(5) \times(-3)]=2+15=17

Let’s find  Adj\left ( A \right )

\begin{aligned} &C_{11}=1, C_{12}=3 \\ &C_{21}=-5, C_{22}=2 \end{aligned}

So,

\begin{aligned} &C_{i j}=\left[\begin{array}{cc} 1 & 3 \\ -5 & 2 \end{array}\right] \\\\ &\operatorname{Adj}(A)=C_{i j}^{T} \\\\ &\operatorname{Adj}(A)=\left[\begin{array}{cc} 1 & -5 \\ 3 & 2 \end{array}\right] \end{aligned}

Let’s put the values in formula

A^{-1}=\frac{1}{17}\left[\begin{array}{cc} 1 & -5 \\ 3 & 2 \end{array}\right]

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