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  • Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 28 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 28 maths textbook solution

Answers (1)

VSQ : 28

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

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

Hint : find adj A and \left | A \right | and then put in A^{-1} formula

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

\left | A \right |=6-5

=1

\left | A \right |\neq 0

So ,A^{-1} exists

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

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

A^{-1}=\frac{adjA}{\left | A \right |}

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

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

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