Question

5. Check which of the following is a magic square. In a magic square, each row, column and diagonal have the same sum. 7 -7 -6 4 -4 2 1 -1 0 -2-3 3 -5 5 6 -8​

Answer 1

Answer:

First for square (i)By adding the numbers in each rows,R1= 5 + (-1) + (-4) = 5 –1 –4 = 5 –5 = 0R2 = -5 + (-2) + 7

= –5 –2 + 7 = -7 + 7 = 0R3= 0 + 3 + (-3) = 3 –3 = 0By adding the numbers in each columns,C1= 5 + (-5) + 0 = 5 –5= 0C2= (-1) + (-2) + 3 = -1 –2 + 3 = -3 + 3 = 0C3 = -4 + 7 + (-3) = -4 + 7 –3 = -7 + 7 = 0By adding the numbers in diagonals,D1= 5 + (-2) + (-3) = 5 –2 –3 = 5 –5 = 0D2= -4 + (-2) + 0= –4 –2 = -6As sum of one diagonal is not equals to zero like the other values,∴, Square (i) is not a magic squareNow, For Square (ii)By adding the numbers in each rows,R1= 1 + (-10) + 0 =1 –10 + 0 = -9R2= (-4) + (-3) + (-2) = -4 –3 –2 = -9R3= (-6) + 4 + (-7) = -6 + 4 –7

13 + 4 = -9By adding the numbers in each columns,C1= 1 + (-4) + (-6) = 1 –4 –6 = 1 –10 = -9C2= (-10) + (-3) + 4 = -10 –3 + 4 = -13 + 4 = -9C3= 0 + (-2) + (-7) = 0 –2 –7 = -9By adding the numbers in diagonals,D1= 1 + (-3) + (-7)= 1 –3 –7 = 1 –10 = -9D2= 0 + (-3) + (-6) = 0 –3 –6 = -9Thus, square (ii) is a magic square, because sum of all row, column and diagonal is equal to -9.