Question

The inverse of the matrix `[(3, 0, 0),(0, 2, 0),(0, 0, 5)]` is ______.

Options

• `[(0, 0, 3),(0, 2, 0),(5, 0, 0)]`

• `[(1/3, 0, 0),(0, 1/2, 0),(0, 0, 1/5)]`

• `[(-1/3, 0, 0),(0, -1/2, 0),(0, 0, -1/5)]`

• `[(-3, 0, 0),(0, -2, 0),(0, 0, -5)]`

Answer 1

The inverse of the matrix `[(3, 0, 0),(0, 2, 0),(0, 0, 5)]` is `underlinebb([(1/3, 0, 0),(0, 1/2, 0),(0, 0, 1/5)])`.

Explanation:

The matrix given is:

`[(3, 0, 0),(0, 2, 0),(0, 0, 5)]`

This is a diagonal matrix.

The inverse of a diagonal matrix is obtained by taking the reciprocal of each diagonal element.

So, `A^-1= [(1/3, 0, 0),(0, 1/2, 0),(0, 0, 1/5)]`