Let A be a non-singular square matrix of order n . Let B be the inverse of A.

**Gauss-Jordan Method**

Let *A *be a non-singular square matrix of order *n *.
Let *B *be the inverse of *A*.

Then, we have *AB *= *BA *= *I _{n} *. By the property of

Consider the equation *A *= *I _{n} A * â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..(1)

Since *A *is non-singular, pre-multiplying by a sequence of
elementary matrices (row operations) on both sides of (1), *A *on the
left-hand-side of (1) is transformed to the identity matrix *I _{n} *and
the same sequence of elementary matrices (row operations) transforms

If *E*_{1} , *E*_{2} ,L, *E _{k} *are
elementary matrices (row operations) such that (

Transforming a non-singular matrix *A *to the form *I _{n}
*by applying elementary row operations, is called

Augment the identity
matrix *I _{n} *on the right-side of

Obtain elementary
matrices (row operations) *E*_{1} , *E*_{2} ,L, *E _{k} *such
that (

Apply *E*_{1}
, *E*_{2} ,L, *E _{k} *on
[

Find the inverse of the non-singular matrix A = , by Gauss-Jordan method.

Applying Gauss-Jordan method, we get

Find the inverse of A = by Gauss-Jordan method.

Applying Gauss-Jordan method, we get

Tags : Definition, Theorem, Formulas, Solved Example Problems | Elementary Transformations of a Matrix , 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants : Gauss Jordan Method | Definition, Theorem, Formulas, Solved Example Problems | Elementary Transformations of a Matrix

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