Question

Let A = [aij] be a square matrix of order 3 such that aij = `hatj - 2hati.` Then which of the following is true?

Options

• a₁₂ > 0

• all aij < 0

• a₁₃ + a₃₁ = −6

• a₂₃ > a₃₂

Answer 1

a₂₃ > a₃₂

Explanation:

A = [aij]^3×3

aij = `hatj - 2hatj`

a₁₂ = 2 − 2(1)

= 0

a₁₃ = 3 − 2(1)

= 1

a₃₁ = 1 − 2(3)

= −5

a₂₃ = 3 − 2(2)

= −1

a₃₂ = 2 − 2(3)

= 4

∴ a₂₃ > a₃₂