Question

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

Answer 1

Given:

• Two 3 × 3 Squares

To Find:

• Weather they are magic squares or not?

Solution:

★ Now,

• We know that a square is called a magic square when each row, column and diagonal have the same sum.

Squares :

A]

$\begin{gathered}\begin{gathered}\begin{gathered} \large\boxed{\begin{array}{c | c | c} {\frak{ \pmb{5}}}&{ - {\frak { \pmb{ 1}}}}&{ - {\frak{ \pmb{4 }}}}\\ \dfrac{}{ - { \frak{ \pmb{5}}}}&\dfrac{}{ - { \frak{ \pmb{ 2}}}}&\dfrac{}{ \: \: { \frak{ \pmb{ 7}}}}& \\ \dfrac{}{ \: \: \: { \frak{ \pmb{0}}}}& \dfrac{}{ \: \: { \frak{ \pmb{3}}}}&\dfrac{}{ - { \frak{ \pmb{ 3}}}}&\end{array}}\end{gathered}& \\ \end{gathered}\end{gathered}$

~ Now let's Check weather it is a magic square or not

Sum of Rows :

➼ 5 + ( - 5 ) + 0 = 0 ✅

➼ - 1 + ( - 2 ) + 3 = 0✅

➼ - 4 + 7 + ( - 3 ) = 0✅

Sum of Columns :

➼ 5 - 1 - 4 = 0✅

➼ - 5 + ( - 2 ) + 7 = 0✅

➼ 0 + 3 + ( - 3 ) = 0✅

Sum of Diagonals :

➼ 5 + ( - 2 )+ ( - 3 ) = 0✅

➼ 0 + ( - 2 ) + ( - 4 ) ≠ 0❌

• Hence it's not a magic square

B]

$\begin{gathered}\begin{gathered}\begin{gathered} \large\boxed{\begin{array}{c | c | c} { \: \: {\frak{ \pmb{1}}}}&{ - {\frak { \pmb{ 10}}}}&{ \: \: {\frak{ \pmb{0 }}}}\\ \dfrac{}{ - \: { \frak{ \pmb{4}}}}&\dfrac{}{ - { \frak{ \pmb{ 3}}}}&\dfrac{}{ - { \frak{ \pmb{ 2}}}}& \\ \dfrac{}{ - \: { \frak{ \pmb{6}}}}& \dfrac{}{ \: \: \: { \frak{ \pmb{4}}}}&\dfrac{}{ - { \frak{ \pmb{ 7}}}}&\end{array}}\end{gathered}& \\ \end{gathered}\end{gathered}$

~ Now let's Check weather it is a magic square or not

Sum of Rows :

➼ 1 + ( - 4) + ( - 6 ) = - 9✅

➼ - 10 - 3 + 4 = - 9✅

➼ 0 - 2 - 7 = - 9✅

Sum of Columns :

➼ 1 - 10 + 0✅

➼ - 4 - 3 - 2 = - 9✅

➼ - 6 + 4 - 7 = - 9✅

Sum of diagonals :

➼ 1 - 3 - 7 = - 9 ✅

➼ - 6 - 3 + 0 = - 9✅

• Henceforth it's a magic square

Answer 2

Answer:

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