Show your own working for this question and i am warning: Only CuriousRose will give answer for this no one will give answer Curiousrose pls also answer my previous question you answer got deleted
In a magic square each row, column and diagonals add up to the same number answer. Check which of the following is a magic square.
Share
Answer:
Figure 2.
Step-by-step explanation:
The only thing required to solve this question -: 'arithmetic operations' i.e. addition (add the like terms / add two or more numbers), which is denoted by the plus (+) symbol and subtraction (subtraction of smaller value from the larger value), which is denoted by the minus (-) symbol. Also, the product of (-)(-) is (+) and (+)(-) is (-). Here we will check if the sum of row is equal to sum of column and diagonal where all the three elements are given. If the sum of row is equal to the sum of column and diagonal, we may say it is a magic square.
To unravel this question, we will first name the rows, columns, and diagonals. Let's call the first row → R1, the second row → R2 and the third row → R3. Similarly, first column → C1, the second column →C2 and the third Column → C3. On the other hand, the first Diagonal → D1 and the second Diagonal → D2.
▫️ FIGURE (1)
On adding the numbers in each row we get,
R1: 1 + (-3) + 2 = 1 - 3 + 2 = 3 - 3 = 0
R2: -4 + 12 + (-8) = - 4 + 12 - 8 = - 12 + 12 = 0
R3: 3 + (-9) + 6 = 3 - 9 + 6 = 9 - 9 = 0
On adding the numbers in each column we get,
C1: 1 + (-4) + 3 = 1 - 4 + 3 = 4 - 4 = 0
C2 -3 + 12 + (-9) = - 3 + 12 - 9 = - 12 + 12 = 0
C3: 2 + (-8) + 6 = 2 - 8 + 6 = 8 - 8 = 0
On adding the numbers in each diagonal we get,
D1: 1 + 12 + 6 = 19
D2: 2 + 12 + 3 = 17
Since, the value of first and second diagonal is 19 and 17 respectively which is not equal to zero. So, the first figure isn't a magic square.
▫️ FIGURE (2)
On adding the numbers in each row we get,
R1: -3 + 4 - 1 = 0
R2: 2 + 0 - 2 = 0
R3: 1 - 4 + 3 = 0
On adding the numbers in each column we get,
C1: - 3 + 2 + 1 = 0
C2: 4 + 0 - 4 = 0
C3: - 1 - 2 + 3 = 0
On adding the numbers in each diagonal we get,
D1: - 3 + 0 + 3 = 0
D2: - 1 + 0 + 1 = 0
Since, the sum of row is equal to the sum of column and diagonal. So, figure (2) is a magic square.
Verified answer
[tex]\huge{\fcolorbox{maroon}{s} {\large{\fcolorbox{white}{mistyrose}{{\fcolorbox{gold} {White}{Answer}}}}}}[/tex]
Refer the attached pic for the reference of rows, columns and diagonals.
Given :
There are two squares given filled with rows and columns of numbers
To find :
We have to check which one of them is a magic square.
Solution :
As it is given that,
In a magic square each row, column and diagonals add up to the same number answer.
So in the first square :--
☆ Adding the rows :-
• Row 1 --> 1 + (-3) + 2 = 0
• Row 2 --> (-4) + 12 + (-8) = 0
• Row 3 --> 3 + (-9) + 6 = 0
☆ Adding the columns :-
• Col. 1 --> 1 + (-4) + 3 = 0
• Col. 2 --> (-3) + 12 + (-9) = 0
• Col. 3 --> 2 + (-8) + 6 = 0
☆ Adding the diagonals :-
• Dia. 1 --> 3 + 12 + 2 = 17
• Dia. 2 --> 1 + 12 + 6 = 19
As each row and column add up to give the same number i.e. 0 but each diagonal is giving different numbers.
So it is not a magic square.
---------------------------------------------------------
Now in the second square :--
☆ Adding the rows :-
• Row 1 --> (-3) + 4 + (-1) = 0
• Row 2 --> 2 + 0 + (-2) = 0
• Row 3 --> 1 + (-4) + 3 = 0
☆ Adding the columns :-
• Col. 1 --> (-3) + 2 + 1 = 0
• Col. 2 --> 4 + 0 + (-4) = 0
• Col. 3 --> (-1) + (-2) + 3 = 0
☆ Adding the diagonals :-
• Dia. 1 --> 1 + 0 + (-1) = 0
• Dia. 2 --> (-3) + 0 + 3 = 0
As each row, column and diagonal add up to give same number i.e. 0.
So it is a magic square.