In a magic square each row, column and diagonal have the same sum. Che

1.	In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.(i) 5-1-4-5-2703-3(ii) 1-100-4-3-2-64-7
Answer» Taking rows 5 + (–1) + (–4) = 5 – 5 = 0 (–5) + (-2) + 7 = –7 + 7 = 0 0 + 3 + (–3) = 3 – 3 = 0 Taking columns 5 + (–5) + 0 = 5 – 5 = 0 (–1) + (–2) + 3 = –3 + 3 = 0 (–4) + 7 + (–3) = 7 – 7 = 0 Taking diagonals 5 + (–2) + (–3) = 5 – 5 = 0 (–4) + (–2) + 0 = –6 This box is not a magic square because all the sums are not equal. (ii) Taking rows 1 + (–10) + 0 = 1 – 10 = –9 (–4) + (–3) + (–2) = –7 – 2 = –9 (–6) + 4 + (–7) = –2 – 7 = –9 Taking columns 1 + (–4) + (–6) = 1 – 10 = –9 (–10) + (–3) + 4 = –13 + 4 = –9 0 + (–2) + (–7) = 0 – 9 = –9 Taking diagonals 1 + (–3) + (–7) = 1 – 10 = –9 0 + (–3) + (–6) = –9 This box is magic square because all the sums are equal.

In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.(i) 5-1-4-5-2703-3(ii) 1-100-4-3-2-64-7

Answer»

Taking rows

5 + (–1) + (–4) = 5 – 5 = 0

(–5) + (-2) + 7 = –7 + 7 = 0

0 + 3 + (–3) = 3 – 3 = 0

Taking columns

5 + (–5) + 0 = 5 – 5 = 0

(–1) + (–2) + 3 = –3 + 3 = 0

(–4) + 7 + (–3) = 7 – 7 = 0

Taking diagonals

5 + (–2) + (–3) = 5 – 5 = 0

(–4) + (–2) + 0 = –6

This box is not a magic square because all the sums are not equal.

(ii)

Taking rows

1 + (–10) + 0 = 1 – 10 = –9

(–4) + (–3) + (–2) = –7 – 2 = –9

(–6) + 4 + (–7) = –2 – 7 = –9

Taking columns

1 + (–4) + (–6) = 1 – 10 = –9

(–10) + (–3) + 4 = –13 + 4 = –9

0 + (–2) + (–7) = 0 – 9 = –9

Taking diagonals

1 + (–3) + (–7) = 1 – 10 = –9

0 + (–3) + (–6) = –9

This box is magic square because all the sums are equal.

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