Question

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 - 2 7

0 3 - 3​

Answer 1

Question :

In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.

$\tt \begin{array}{|c|c|c|} 5 & -1 & -4 \\ -5 & -2 & 7 \\ 0 & 3 & -3 \\ \end{array}$

Solution :

Sum of first row = 5 - 1 - 4 = 5 - 5 = 0

Sum of second row = - 5 - 2 + 7 = - 7 + 7 = 0

Sum of third row = 0 + 3 - 3 = 3 - 3 = 0

Sum of first column = 5 - 5 + 0 = 5 - 5 = 0

Sum of second column = - 1 - 2 + 3 = - 3 + 3 = 0

Sum of third column = - 4 + 7 - 3 = 3 - 3 = 0

Sum of one diagonal = 5 - 2 - 3 = 5 - 5 = 0

Sum of other diagonal = - 4 - 2 + 0 = - 6

Hence it is not a magical square.

Answer 2

Answer:

Question :

In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.

$\tt \begin{array}{|c|c|c|} 5 & -1 & -4 \\ -5 & -2 & 7 \\ 0 & 3 & -3 \\ \end{array}$

Solution :

Sum of first row = 5 - 1 - 4 = 5 - 5 = 0

Sum of second row = - 5 - 2 + 7 = - 7 + 7 = 0

Sum of third row = 0 + 3 - 3 = 3 - 3 = 0

Sum of first column = 5 - 5 + 0 = 5 - 5 = 0

Sum of second column = - 1 - 2 + 3 = - 3 + 3 = 0

Sum of third column = - 4 + 7 - 3 = 3 - 3 = 0

Sum of one diagonal = 5 - 2 - 3 = 5 - 5 = 0

Sum of other diagonal = - 4 - 2 + 0 = - 6

Hence it is not a magical square.