Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top


det $\begin{bmatrix} r & s & t \\ u & v & w \\ x & y & z \\ \end{bmatrix}=4$, compute det $\begin{bmatrix}r&s&s\\x-8r&y-8s&z-8t\\8u&8v&8w\end{bmatrix}$

How should I start going about this problem? I'm not sure how exactly the determinants of the two matrices are related.

share|cite|improve this question
up vote 3 down vote accepted

The determinant satisfies several properties:

  1. If you multiply a single row by a scalar, it multiplies the determinant by that scalar.
  2. If you swap two rows, it flips the sign of the determinant.
  3. If you add a multiple of one row to another row, it doesn't change the determinant.

Using these three properties, try to find a way to use those three operations to turn your first matrix, whose determinant you know, into the new matrix.

share|cite|improve this answer

Note that row 3 was exchanged with $8 \times$ row 2:

  • How does exchanging a row affect the determinant?
  • How does multiplying a row by 8 affect the determininant of the matrix?

Then $-8 \times$ row 1 was added to the (exchanged) row 2.

  • How does adding a multiple of a row by affect the determinant?

These are elementary row operations which transform the determinant of the original matrix.

share|cite|improve this answer
Thanks, that's just what I was looking for. – Chris A Feb 26 '13 at 20:25
Good: It just takes a little "backwards thinking" to backtrack and see which row operations were performed. – amWhy Feb 26 '13 at 20:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.