00:01
In this question, we are asked to use determinants to determine if the given set of vectors is linearly independent.
00:08
Now, recall that let the vectors be v1, v2, and v3.
00:16
And let a be a matrix whose columns are the vectors v1, v2, and v3.
00:25
Then the vectors, if the determinant of a equals to 0, then the vectors are linearly dependent.
00:47
If the determinant is non -zero, then the vectors are linearly independent.
00:57
Therefore, the problem has been reduced to calculating the determinant of the matrix a.
01:24
To calculate this determinant, choose the row, we will use the co -factor expansion across a row or a column of the matrix.
01:35
And the best way to apply this method is to choose a row or a column which has the most zeros.
01:43
And in our case, we have only one row which has 1 -0 and one column which has 1 -0.
01:52
We can choose, for example, the co -factor expansion across the second row because it contains a 0.
02:02
To do that, we will take, we need to do negative 1 and the power of negative 1 will be equal to the...
02:12
So, first we will do...
02:15
Will cross out the second row and the first column.
02:21
The element on the intersection is 2, and the number, the position of the element at the intersection is second row and first column.
02:35
Therefore, the power of negative 1 will be equal to 2 plus 1, second row plus 1 column, times the entry at the intersection, times the determinant of the sub -matrix...