Using elementary row operations, find the inverse of the following matrix:
$[\begin{matrix} 2 & 5 \\ 1 & 3 \end{matrix}]$

Solution

$Let A = [\begin{matrix} 2 & 5 \\ 1 & 3 \end{matrix}]$

We can write A = IA

$i . e . [\begin{matrix} 2 & 5 \\ 1 & 3 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] A Applying R_{1} \to \frac{1}{2} R_{1}, we get [\begin{matrix} 1 & \frac{5}{2} \\ 1 & 3 \end{matrix}] = [\begin{matrix} \frac{1}{2} & 0 \\ 0 & 1 \end{matrix}] A Applying R_{2} \to R_{2} - R_{1}, gives [\begin{matrix} 1 & \frac{5}{2} \\ 0 & \frac{1}{2} \end{matrix}] = [\begin{matrix} \frac{1}{2} & 0 \\ \frac{- 1}{2} & 1 \end{matrix}] A Applying R_{1} \to R_{1} - 5 R_{2}, we obtain [\begin{matrix} 1 & 0 \\ 0 & \frac{1}{2} \end{matrix}] = [\begin{matrix} 3 & - 5 \\ \frac{- 1}{2} & 1 \end{matrix}] A Applying R_{2} \to 2 R_{2}, gives [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} 3 & - 5 \\ - 1 & 2 \end{matrix}] A Therefore, A^{- 1} = [\begin{matrix} 3 & - 5 \\ - 1 & 2 \end{matrix}]$

Some More Questions From Matrices Chapter

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Matrices

Using elementary row operations, find the inverse of the following matrix:
$[\begin{matrix} 2 & 5 \\ 1 & 3 \end{matrix}]$

Some More Questions From Matrices Chapter

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

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For Daily Free Study Material Join wiredfaculty

Matrices

Using elementary row operations, find the inverse of the following matrix: 2 51 3

Some More Questions From Matrices Chapter

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Using elementary row operations, find the inverse of the following matrix:
$[\begin{matrix} 2 & 5 \\ 1 & 3 \end{matrix}]$