Question

Verify using an example that a(b+c) is not equal to ab+ac. (This means that addition does not distribute over the dot product.)

My solution: is this correct?

a(b+c)= ab+ac is ALWAYS true for whatever numbers you substitute

let a = 16
b = 3
and c = 5
so LHE = a/(a + b) = 16 / (3 + 5) = 16/8 = 2
and RHE = (a/b) + (a/c) = (16/3) + (16/5) ≠ 2
so a/(a + b) ≠ (a/b) + (a/c)
LHE = a + (bc) = 16 + 3 x 5 = 16 + 15 = 31
RHE = (a + b)(a + c) = (16 + 3)(16 + 5) = 19 x 21 ≠ 31
so a + (bc) ≠ (a + b)(a + c)

Answer 1

http://www.cliffsnotes.com/math/algebra/linear-algebra/matrix-algebra/operations-with-matrices