Word Count : 384

---

To show that the set of vectors \( a_1 = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}, a_2 = \begin{bmatrix} 2 \\ 0 \\ 2 \end{bmatrix}, a_3 = \begin{bmatrix} 0 \\ 2 \\ 3 \end{bmatrix} \) forms a basis for \( \mathbb{R}^3 \), we need to check if these vectors are linearly independent. If they are linearly independent, they will form a basis for \( \mathbb{R}^3 \). ### Step 1: Set up the linear dependence equation. We need to check if the only solution to the equation \[ c_1 a_1 + c_2 a_2 + c_3 a_3 ___ ________ ___ ________ ___ ________ __________.
__________ _______ ______ __________ ______ _________ _______ ____ _________.
___ ____ _____ ________ _______ _______ ______ ______ ___.
__________ ______ ___ ___ ____ _______ __________.
________ ____ ________ _________ __________ ___ ______ ____ _____ _____ ____ ________.
__________ __________ _____ _____ ____ _____ _______ ________ ___ _____ _______ ________.
______ __________ ______ __________ __________ _________.
_____ ________ ___ ______ __________ __________ ______.
________ __________ ______ ___ ________ _____ __________ ______ _________ ____ __________.
________ __________ ____ __________ ________ __________ ___.
_______ ______ _______ ____ ________ __________ ____ _______.
__________ _________ ___ _________ ______ ______ ______ ______ ____ ____.
__________ _____ ______ ___ ________.
_______ ______ ___ ___ _________ ________ ___ ____ ______ ____.
_____ _________ ____ ______ _________ _________ _____ ___ _______ ______.
_______ ___ ______ ____ ___ _____ ______.
_________ ___ ___ _____ _____ ___.
____ _____ ___ ________ __________ ___ ______ _____ _________ ____ ____.
_____ ____ _________ ______ ________ _________ ________ _________ _______ ___.
_____ _______ ______ __________ _______ _________ ______ ______.
_______ _____ ______ ___ __________ __________ ____ ___ ______ ________ ________ _______.
______ ________ _________ __________ ____.
_________ ___ ___ _________ ______ ____ ____ __________ ______ ___.
___ _____ _____ ______ _________ ___ ___ __________ ___.
_________ _____ _____ _________ __________ ______ _____ __________ ______ ________ ________.
____ _______ _____ _________ ________ _______.
___ ___ ___ _________ ________ ________ ___ _____ _______.
_________ ____ ______ _____ __________ ______.
___ __________ _______ ______ __________ _________ __________ ___.
_________ _______ ________ ____ _______ ___ ______ ______ ____ ___.
______ ___ ____ _________ ___ ___ __________ _________.
____ ______ ________ _______ ______.
_______ _______ ________ ____ ________ _________ _________ ______ ________ _______ __________ ____.
____ ________ _________ __________ ______.
Get Full Answer on WhatsApp