Question

`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|` = ______.

Options

• a + b + c

• 2a + b + c

• ab + bc + ca

• 4abc

Answer 1

`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|` = 4abc.

Explanation:

`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|`

Applying C₁→C₁ + C₂ + C₃

`|(2("b" + "c"), "c", "b"),(2("c" + "a"), "c" + "a", "a"),(2("a" + "b"), "a", "a" + "b")|`

Applying C₁→C₁ – C₂

`2|("b", "c", "b"),(0, "c" + "a", "a"),("b", "a", "a" + "b")|` = `2"b"  |(1, "c", "b"),(0, "c" + "a", "a"),(1, "a", "a" + "b")|`

= `2"b"|(0, "c" - "a", -"a"),(0, "c" + "a", "a"),(1, "a", "a" + "b")|` Applying R₁→R₁ – R₃

= 2b{a(c – a) + a(c + a)}

= 2b{ac – a² + ac + a²}

= 4abc