Question

Construct a_{2 × 2} matrix where a_ij = |–2i + 3j|

Answer 1

Let A = `[("a"_13, "a"_12),("a"_21, "a"_22)]_(2  xx 2)`

Given that `a_ij = |–2i + 3j|

a₁₁ = |–2 × 1 + 3 × 1| = 1

a₁₂ = |–2 × 1 + 3 × 2| = 4

a₂₁ = |–2 × 2 + 3 × 1| = –1

a₂₂ = |–2 × 2 + 3 × 2| = 2

Hence, the matrix A = `[(1, 4),(-1, 2)]`