Question

Construct a 3 × 4 matrix A = [a_jj] whose elements a_jj are given by:

a_jj = i − j

Answer 1

Let A = [a_ij]2 × 3

So, the elements in a 3 × 4 matrix are

a₁₁, a₁₂, a₁₃, a₁₄, a₂₁, a₂₂, a₂₃, a₂₄, a₃₁, a₃₂, a₃₃, a₃₄

a₁₁ = 1 − 1 = 0 a₁₂ = 1 − 2 = −1 a₁₃ = 1 − 3 = −2 a₁₄ = 1 − 4 = −3

a₂₁ = 2 − 1 = 1 a₂₂ = 2 − 2 = 0 a₂₃ = 2 − 3 = −1 a₂₄ = 2 − 4 = −2

a₃₁ = 3 − 1 = 2 a₃₂ = 3 − 2 = 1 a₃₃ = 3 − 3 = 0 a₃₄ = 3 − 4 = −1

So, from (1)