Question 211750
For matrix B, the key is to notice that row 4 is exactly twice row 1. In such a matrix the determinant is always zero.<br>
Both matrices C and D are diagonal matrices (i.e. a matrix with nothing but zeros above and/or below the main diagonal). In diagonal matrices the determinant is simply the product of the numbers in the diagonal. For C this would be {{{2*2*4 = 16}}}. For D this would be {{{-3*2*-5 = 30}}}.<br>
If you need more "reasons"...<br>
For matrix B, think about adding -2 times the first row to the fourth row. This type of operation does not change the value of the determinant and, in this casse, it results in row 4 becoming all zeros. Then think about finding the value of the determinant using the fourth row. Result: 0.<br>
For matrices C and D, think about using the first column to find the value of the determinant. Since there is only one non-zero value in this column, it should be easy to visualize the calculations and see why only the product of the numbers in the diagonal will matter.