Question

The number of solutions of equation x₂ – x₃ = 1, – x₁ + 2x₃ = 2, x₁ – 2x₂ = 3 is ______.

विकल्प

• zero

• one

• two

• infinite

Answer 1

The number of solutions of equation x₂ – x₃ = 1, – x₁ + 2x₃ = 2, x₁ – 2x₂ = 3 is zero.

Explanation:

The system is 0x₁ + x₂ – x₃ = 1

– x₁ + 0x₂ + 2x₃ = 2

x₁ – 2x₂ + 0x₃ = 3

`\implies [(0, 1, -1),(-1, 0, 2),(1, -2, 0)][(x_1),(x_2),(x_3)] = [(1),(2),(3)]` or AX = B

Clearly |A| = 0

Now Adj A = `[(4, 2, 2),(2, 1, 1),(2, 1, 1)]`

∴ (Adj A) B ≠ 0

`\implies` system is inconsistent