Question

| 10 24 36 |
| 36 10 24 |
| 24 36 10 |
Show that
Is divisible by 35

Answer 1

Given:

Given matrix is

$\left[\begin{array}{ccc}10&24&36\\36&10&24\\24&36&10\end{array}\right]$

To find:

If given matrix is divisible by 35

Solution:

• To understand how to find determinant of a matrix lets take a sample matrix first as follows

• $\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]$  

• Above matrix has determinant value,

• D = a ( e*i - f*h) -b(d*i - f*g) + c(d*h - g*e)
• Similarly given matrix has
• D = 10 (10*10 - 36*24) -24(36*10 - 24*24) + 36 (36*36 - 24*10)
• D = 10(-764) -24(-216) + 36(1056)
• D = -7640 + 5184 + 38016
• D = 35,560
• Now, we have to check whether D is divisible by 35
• 35560/35 = 1016
• Hence, Determinant is divisible by 35.

Answer:

Hence, given matrix is divisible by 35.