Question

If `Δ_1 = |(1  0  0), (0  2  0), (0  0  3)| and Δ_2 = |(0  2  0), (1  0  0), (0  0  6)|`, then ______.

Options

• Δ₁ = 2Δ₂

• Δ₂ = −2Δ₁

• Δ₁ = Δ₂

• Δ₂ = −Δ₁

Answer 1

If `Δ_1 = |(1  0  0), (0  2  0), (0  0  3)| and Δ_2 = |(0  2  0), (1  0  0), (0  0  6)|`, then Δ₂ = −2Δ₁.

Explanation:

Δ₂ is obtained by interchanging the first two rows of Δ₁, which changes the sign, and also multiplying one row by 2, which multiplies the determinant by 2.

Hence, overall Δ₂ = −2Δ₁.