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If the determinant of the matrix | a 5x p | | b 10y 5 | | c 15 15 | is 125, then what is the value of the determinant | 3a 3b c | | x 2y z | | p 5 5 | ?
- 25
- 125
- 5
- 10
Correct answer: 5
Solution
The determinant of a matrix scales by the product of the factors used to multiply its rows or columns. In this case, the first row is multiplied by 3, the second row by 1, and the third row by 1, resulting in a scaling factor of 3. Since the determinant of the original matrix is 125, the new determinant is calculated as 125 divided by 3, which simplifies to 5.
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