What is the determinant of the coefficient matrix of the system 0 16 18 40

The coefficient matrix is

Notice that the last row is -4 times the first row, so that the rows of the matrix are not independent. This means the determinant would be 0.

Just to confirm, we can compute the determinant via a Laplace expansion along the first row:

step-by-step explanation: noo

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2