Question

Evaluate: `|("a" + x, y, z),(x, "a" + y, z),(x, y, "a" + z)|`

Answer 1

We have `|("a" + x, y, z),(x, "a" + y, z),(x, y, "a" + z)|`

[Applying C₁ → C₁ + C₂ + C₃]

= `|("a" + x + y + z,y, z),("a" + x + y + z, "a" + y, z),("a" + x + y + z, y, "a" + z)|`

= `("a" + x + y + z)|(1, y, z),(1, "a" + y, z),(1, y, "a" + z)|`

[Applying R₂ → R₂ – R₁ and R₃ → R₃ – R₁]

= `("a" + x + y + z)|(1, y, z),(0, "a", 0),(0, 0, "a")|`

= `("a" + x +y + z)|("a", 0),(0, "a")|`

= a²(a + z + x + y)