IPMAT Indore 2024 - QA (SA) Q15 Explanation

Explanation:

(288) Let A =[ 𝑥1 𝑥2 7 𝑦1 𝑦2 𝑦3 𝑧1 8 3 ] = [ 𝑎 𝑏 7 𝑐 𝑑 𝑒 𝑓 8 3 ]

Let the sum of all three elements along any row, column or diagonal be S.

Then, f = S –(8+3) = S -11 …eqn.(i) (from the bottom row)

d = S – (7+ f) …eqn.(ii) (from one of the diagonals)

From equations (i) and (ii),

we get d = S– (7 +S -11)

∴ d = 4

Also, b = S –(8+d) = S – 12 (from the middle column) …eqn.(iii)

a = S– (b +7) (from the first row)…eqn.(iv)

From equations (iii) and (iv),

we get a = 5 & b = 0

∴S=12

∴The matrix A comes out to be = [ 5 0 7 6 4 2 1 8 3 ]

Determinant |A| = 5(4×3−8×2)+0(2×1−6×3)+ 7(6×8−1×4) = 5(12−16)+0+7(48−4) = −20+0+308=288 Ans.