Question

if `|(a, b, c),(m, n, p),(x, y, z)| = k`, then what is the value of `|(6a, 2b, 2c),(3m, n, p),(3x, y, z)|`?

विकल्प

• `k/6`

• 2k

• 3k

• 6k

Answer 1

6k

Explanation:

Given:

`|(a, b, c),(m, n, p),(x, y, z)| = k`

We want to find:

`|(6a, 2b, 2c),(3m, n, p),(3x, y, z)|`

Applying the Scaling Rule

1. The first row is scaled by 6, 2 and 2 for a, b and c respectively. This results in a scaling factor of 6 × 2 × 2 = 24.
2. The second row is scaled by 3 for m. This results in an additional scaling factor of 3.
3. The third row is scaled by 3 for x. This results in an additional scaling factor of 3.

So, the total scaling factor is:

24 × 3 × 3 = 216

However, we need to scale the entire first row by 2 to maintain the proportions:

`|(6a, 2b, 2c),(3m, n, p),(3x, y, z)| = 6 * |(6a, 2/6b, 2/6c),(m, 1/3n, 1/3p),(3x, 1/3y, 1/3z)|`

Therefore, the value of the determinant is:

= `6|(a, b, c),(m, n, p),(x, y, z)|`

= 6k