## Check If The Following Vector Is Linearly Independent Or Not

In order to find the determinatn of a matrix, the elements should be separated by commas and rows by curly braces, brackets, or parentheses. In a n x n matrix, the minors are determinants of (n-1) x (n-1) matrices. To find the determinant, the row or column with the most 0 elements should be chosen. The video explains how to find the determinant of a 3x3 matrix. The determinant can be found by choosing a single row or column, crossing out that row and column, and finding the determinant of the remaining 2x2 matrix. In order to support the work on finding the determinant, a step-by-step guide is given, along with an example.

To check whether the vectors (0,1,5), (1,2,8), and (4,-1,0) are linearly independent or not, we can use the concept of determinants.

For three vectors to be linearly independent, the determinant formed by arranging these vectors as the rows of a matrix should be non-zero.

Let's form the matrix A with the given vectors as rows: A = | 0 1 5 | | 1 2 8 | | 4 -1 0 |

To find if the vectors are linearly independent, we need to calculate the determinant of matrix A. The determinant of matrix A can be found using the following formula: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)

where a, b, and c are the elements of the first row, and d, e, and f are the second row elements, and g, h, and i are the third row elements.

Let's calculate the determinant of matrix A to determine if the vectors are linearly independent.

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