Question

Construct a 3 × 4 matrix, whose elements are given by:

a_ij = 2i − j

Answer 1

In general, a 3 × 4 matrix is given by A = `[(a_11, a_12,a_13,a_14), (a_21,a_22, a_23, a_24), (a_31,a_32, a_33, a_34)]`

⇒ a_ij = 2i − j, i = 1, 2, 3 and j = 1, 2, 3, 4

a₁₁ = 2 × 1 − 1

= 2 − 1

= 1

a₂₁ = 2 × 2 − 1

= 4 − 1

= 3

a₃₁ = 2 × 3 − 1

= 6 − 1

= 5

a₁₂ = 2 × 1 − 2

= 2 − 2

= 0

a₂₂ = 2 × 2 − 2

= 4 − 2

= 2

a₃₂ = 2 × 3 − 2

= 6 − 2

= 4

a₁₃ = 2 × 1 − 3

= 2 − 3

= −1 

a₂₃ = 2 × 2 − 3

= 4 − 3

= 1

a₃₃ = 2 × 3 − 3

= 6 − 3

= 3

a₁₄ = 2 × 1 − 4

= 2 − 4

= −2

a₂₄ = 2 × 2 − 4

= 4 − 4

= 0

a₃₄ = 2 × 3 − 4

= 6 − 4

= 2

Therefore, the required matrix is A = `[(1,0,-1,-2),(3,2,1,0),(5,4,3,2)]`