Find a 3x3 matrix (if one exists) that has eigenvalues 1, 2, 3 and a determinant of 4.

linear-algebra determinant eigenvalues-eigenvectors

How would you go about figuring out if this matrix exists (and if it does, providing an example)

I would understand how to do this with a 2x2 matrix, as the determinant is easily calculable. With a 3x3 matrix, I feel there are many factors to control that make the problem difficult.

Since this was given as a subquestion on a test, I know there is a quick way to figure out that this exists/doesn't, but I can not seem to find it.


Per @azimut 's comment, the determinant of a matrix is the product of the eigenvalues, so it is obvious that one does not exist as $1*3*2\neq4$

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