Using elementary row transformations, find the inverse of the following matrices: [(1,2,3)(2,5,7)(-2,-4,-5)]

Question

Using elementary row transformations, find the inverse of the following matrices:

\( \begin{bmatrix} 1 & 2 & 3 \\[0.3em] 2& 5 &7 \\[0.3em] -2 & -4 &-5 \end{bmatrix}\)

[(1,2,3)(2,5,7)(-2,-4,-5)]

Answer 1

Let, A = \( \begin{bmatrix} 1 & 2 & 3 \\[0.3em] 2& 5 &7 \\[0.3em] -2 & -4 &-5 \end{bmatrix}\)

Now we are going to write the Augmented Matrix followed by matrix A and the Identity matrix I, i.e.,

Now our job is to convert the matrix A into Identity Matrix. 

Therefore, the matrix we will get converting the matrix I will be our A^-1.

Here, the matrix A is converted into Identity matrix. 

Therefore, we get the A^-1 as,

The value of A^-1 is correct or not can be verified by the formula: AA^-1 = I