2) Compute the determinants of the following 4×4 matrices as linear combinations of the determinants of some 3×3 matrices, i.e. "magic formula" for expanding a determinant by "minors": 3 1 4 5 6 2 3 4 5678 9 8 7 6 You see how the "magic formula" is computationally inefficient as the size of the matrix grows, whereas elementary matrices are very efficient!

Suppose we wish to compute the determinant of 7-3 0 A--2 1 -5 1 by cofactor expansion on row 1. What is that expansion? det(A) And what is the value of that determinant?

1. Can we use cofactor expansion in a 2 x 2 matrix? 2. What is the determinant of a 1x 1 matrix?

I got the attached question wrong on a quiz, but don't understand why my answer choice ("selected answer") is not correct.  I think the right answer is the choice about having 4 pivot points.  Can you explain why my original choice is also not valid?   Note:  I do know that a matrix can have a nonzero rows, but still have a determinant of 0, thus not invertible.  However, this question is talking about the nonzero rows in the row-echelon form.   Thanks!