Word Count : 241

---

To determine the values of \( k \) for which the given vectors are linearly independent, we need to check when the determinant of the matrix formed by these vectors as columns is nonzero. ### Step 1: Form the Matrix The given vectors are: \[ \mathbf{v_1} = \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix}, \mathbf{v_2} = \begin{bmatrix} 1 \\ k ____ _______ ___ ____ _____ ___ ______ ________ ______ ______ _________.
________ _______ __________ __________ _____ ______ ___ ______ _____ _____.
_________ _____ ____ ______ _______ ______ ___ _________ __________ ______ ______ ___.
__________ ___ ______ __________ _______ ___ __________ ________ ________ ______ _____.
______ _______ _______ ____ _________ ________ _______ _________ ___ ___ ________.
__________ ______ ________ ______ ____ _____ __________.
____ _____ _______ ___ _________ _________ ___ ________ __________ _______ _______.
__________ _______ ___ ______ _____ ____.
____ _______ ________ ____ ___.
______ _______ ______ ___ _______ ______ ______.
___ _____ ___ _____ _____ _____ _______ ____ ____ ____.
________ __________ ______ _____ ___ __________ ______.
_______ _______ __________ ____ __________ ________ _______ ________ ___.
______ _____ ____ ______ _________ _________.
_______ _______ ________ ____ __________ _______ ____ ___ _____.
___ ___ __________ _________ _______ _______.
______ ____ ____ _____ _________ _____ __________ ___ ____.
_______ ______ _______ _________ _______ ______ ___ ______ _______.
_____ ____ __________ ______ ________ ______ _________ _________ ______ ____ ______ ____.
_________ ______ ___ _____ ________ __________ _______ _____.
_______ ___ __________ ________ ___.
Get Full Answer on WhatsApp