Question

Find cofactors of the elements of the matrix A = `[(-1, 2),(-3, 4)]`.

Answer 1

Given A = `[[-1,2],[-3,4]]` 

Step 1: Understand the Cofactor Definition

For a 2×2 matrix:

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

The cofactor matrix is:

Cof(A) `[(+d, -c),(-b, +c)]`

Step 2: Identify values

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

• a = −1
• b = 2
• c = −3
• d = 4

Step 3: Compute cofactors

Now apply the formula:

• Cofactor of a = −1 → + d = +4
• Cofactor of b = 2 → −c = −(−3) = +3
• Cofactor of c = −3 → −b = −2
• Cofactor of d = 4 → +a = −1

Step 4: Write the Cofactor Matrix 

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