Question

If A = `[(2, -4),(3, 1)]`, then the adjoint of matrix A is ______.

Options

• `[(-1, 3),(-4, 1)]`

• `[(1, 4),(-3, 2)]`

• `[(1, 3),(4, -2)]`

• `[(-1, -3),(-4, 2)]`

Answer 1

If A = `[(2, -4),(3, 1)]`, then the adjoint of matrix A is `underlinebb([(1, 4),(-3, 2)])`.

Explanation:

Given:

A = `[(2, -4),(3, 1)]`

Step 1: Formula for adjoint of a 2 × 2 matrix

For a martix

A = `[(a, b),(c, d)]`

The adjoint (adj A) is:

adj (A) = `[(d, -b),(-c, a)]`

Step 2: Identify values

Here,

a = 2

b = – 4

c = 3

d = 1

Step 3: Apply formula

adj (A) = `[(1, -(-4)),(-3, 2)]`

= `[(1, 4),(-3, 2)]`