# Calculating determinant after multiple row operations?

I have exhausted everything I know about solving for the determinant after operations have been done to it following the general principles of matrix determinants.

I see that the first row was multiplied by a scalar and the second row was multiplied by a scalar. It was my general assumption that I would take the original determinant and multiply by the first scalar and then add the original times the scalar multiplied by the second row. Obviously got the wrong answer and feel like I am missing something very basic here. Thanks for the assistance.

## 1 Answer

Hint: If $$A = \pmatrix{ v_1\\ v_2\\ v_3\\ v_4 }$$ Then $$\pmatrix{ 9v_1 + 3v_2\\ 4v_1 + 8v_2\\ v_3\\ v_4 } = \pmatrix{ 9&3&0&0\\ 4&8&0&0\\ 0&0&1&0\\ 0&0&0&1 } A$$ How can we find the determinant of this product?

• I found the determinant and got 60. Am I missing your point? Commented Feb 3, 2014 at 2:15
• Has your class covered the formula $\det(AB) = \det(A) \det(B)$? Commented Feb 3, 2014 at 2:18
• No, but I looked it up online. Am I looking for det(B) * det(A)? Commented Feb 3, 2014 at 2:19
• The original question is wrong. You should conclude that the determinant of the matrix is -120. The answer is correct. Commented Feb 3, 2014 at 2:19
• Yes, I got negative 120 from taking the determinant of the system given and then multiplying it by the original det(A). Thank Omnomnomnomnomnom Commented Feb 3, 2014 at 2:20