Question

The inverse of the matrix X = `[(2, 0, 0),(0, 3, 0),(0, 0, 4)]` is ______.

Options

• `24[(1//2, 0, 0),(0, 1//3, 0),(0, 0, 1//4)]`

• `1/24[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

• `1/24[(2, 0, 0),(0, 3, 0),(0, 0, 4)]`

• `[(1//2, 0, 0),(0, 1//3, 0),(0, 0, 1//4)]`

Answer 1

The inverse of the matrix X = `[(2, 0, 0),(0, 3, 0),(0, 0, 4)]` is `underlinebb([(1//2, 0, 0),(0, 1//3, 0),(0, 0, 1//4)])`.

Explanation:

The inverse of a diagonal matrix is created by replacing each diagonal element with its reciprocal.

Since, `X = [(2, 0, 0),(0, 3, 0),(0, 0, 4)]`

Therefore `X^-1 = [(1/2, 0, 0),(0, 1/3, 0),(0, 0, 1/4)]`