Question

Construct a 3 × 3 matrix whose elements are given by a_ij = |i – 2j|

Answer 1

a_ij = |i – 2j|

The general 3 × 3 matrices is

A = `[("a"_11, "a"_12, "a"_13),("a"_21, "a"_22, "a"_23),("a"_31, "a"_32, "a"_33)]`

a₁₁ = |1 – 2(1)| = |1 – 2| = | – 1| = 1

a₁₂ = |1 – 2(2)| = |1 – 4| = | – 3| = 3

a₁₃ = |1 – 2(3)| = |1 – 6| = | – 5| = 5

a₂₁ = |2 – 2(1)| = |2 – 2| = 0 = 0

a₂₂ = |2 – 2(2)| = |2 – 4| = | – 2| = 2

a₂₃ = |2 – 2(3)| = |2 – 6| = | – 4| = 4

a₃₁ = |3 – 2(1)| = |3 – 2| = |1| = 1

a₃₂ = |3 – 2(2)| = |3 – 4| = | – 1| = 1

a₃₃ = |3 – 2(3)| = |3 – 6| = |– 3| = 3

The required matrix A = `[(1, 3, 5),(0, 2, 4),(1, 1, 3)]`