00:01
In this question, we are told that a is a 4 by 4 matrix and the determinant of a equals to 8.
00:07
And for clarity, we will write a in the given form, where a1, a2, a3 and a4 are row vectors.
00:19
A1 equals and each of a1, a2, a3 and a4 consists of 4 is a row of 4 entries, right? that's just for convenience.
00:29
Then we are asked to find the determinant of the three of the following three matrices b, c and d.
00:38
And the matrix b is obtained from a by adding 5 times the second row to the first row and to calculate the determinant of b we will use the linearity property of determinants in other words, the determinant of this matrix equals to the sum of two determinants the determinant of a1, a2, a3 and a4, plus the determinant of 5a2, a2, a3, and a4.
01:40
Now, recall that these are matrices, right? these are not columns, because each a is a row vector.
01:49
It has four entries.
01:55
And this equals the first is simply the determinant of the matrix a and equals to 8 because a1, a2, a3 and a4 is the matrix a right? and the second matrix has two rows which are multiples of each other.
02:20
The first row is a multiple of the second row, right? and this means that its determinant is zero...