A matrix is invertible iff. the . What happens if a column of row is alls zeros?

Definition:

The determinant of an nxn matrix A, denoted det(A), is a scalar associated with the matrix A that is defined inductively as

where are the cofactors associated with the entries in the first row of A.

Leon, S. (2010).Linear algebra with applications. Upper Saddle River, NJ: Pearson.

a.

By expanding across the row of all zeros, each term of the cofactor expansion will have a factor of 0. Hence, the sum will equal