"1) If the determinant of a 5 x 5 matrix A is det(A) = 8, and the matrix B is obtained from A by multiplying the second row by 2, then det(B) = ?
2) If the determinant of a 4 x 4 matrix A is det(A) = 5, and the matrix C is obtained from A by swapping the third and fourth rows, then det(C) = ?
3) If the determinant of a 5 x 5 matrix A is det(A) = 6, and the matrix D is obtained from A by adding 4 times the third row to the second, then det(D) = ?"
My problem is not getting the new determinant but rather finding a matrix that satisfies the original determinant. Is there a formula through which I can find the matrix given its determinant, because computing the determinant of the new matrix should not be a problem.
Thank you!
Best Answer
Hint
In 1), we have $$B=\begin{pmatrix}1&0&0&0&0\\0&2&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&1\end{pmatrix}A$$
Can you solve the other parts in a similar way?