Question

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

विकल्प

• `[(1,3),(-4,2)]`

• `[(1,-3),(-4,2)]`

• `[(1,3),(4,-2)]`

• `[(-1,-3),(-4,2)]`

Answer 1

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

Explanation:

We are given a 2 × 2 matrix:

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

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

`A = [(a, b),(c, d)]`, the adjoint is: adj (A) = `[(d, -b),(-c, a)]`

Step 2: Apply to our matrix

Given: 

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

So: 

• a = 2
• b = −3
• c = 4
• d = 1

Now compute the adjont: 

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