BrutusAI Result: Are These Vectors Linearly Dependant (0,1,5),(1,2,8),(4, 1,0)

Are These Vectors Linearly Dependant (0,1,5),(1,2,8),(4, 1,0)

Text snippet: This text provides information on calculating the determinant of a 3x3 matrix. It explains the process of finding three products by choosing any row or column of the matrix and breaking down the matrix into smaller secondary matrices. A step-by-step method is also available through a free online calculator. Additionally, a video tutorial is provided for finding the determinant of a 3x3 matrix.

To determine if the given vectors are linearly independent, we can create a matrix with the given vectors as its rows and then calculate its determinant.

Consider the vectors as rows of a matrix M: M = | 0 1 5 | | 1 2 8 | | 4 -1 0 |

Now, we can calculate the determinant of this matrix to determine linear independence. The vectors are linearly independent if and only if the determinant of the matrix is non-zero.

Calculating the determinant using the method for a 3x3 matrix, we get: det(M) = 0(20 - 8(-1)) - 1(10 - 84) + 5(1*(-1) - 2*4) = 0 - 32 + 5(-1 - 8) = 0 - 32 - 45 = -77

Since the determinant is not zero (-77), the vectors are linearly independent.

Sources

The Formula of the Determinant of 3×3 Matrix - ChiliMath Determinant of a 3x3 matrix: standard method (1 of 2) (video) - Khan Academy Determinant of a Matrix - Math is Fun [PDF] The determinant of a 3 × 3 matrix - Mathcentre Determinant Calculator - Matrix Calculator - Reshish How To Find The Determinant of a 3x3 Matrix - YouTube

Are These Vectors Linearly Dependant (0,1,5),(1,2,8),(4, 1,0)

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Are These Vectors Linearly Dependant (0,1,5),(1,2,8),(4, 1,0)

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