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Math  /  Algebra

QuestionQuestion 4 [10 points] Determine all values of aa for which the following set of vectors is dependent or independent. You can select 'always', 'never', ' a=a= ', or ' a≠a \neq ', then specify a value or comma-separated list of values. {[a1−2−3],[261−5],[4−8−10−2]}\left\{\left[\begin{array}{c} a \\ 1 \\ -2 \\ -3 \end{array}\right],\left[\begin{array}{c} 2 \\ 6 \\ 1 \\ -5 \end{array}\right],\left[\begin{array}{c} 4 \\ -8 \\ -10 \\ -2 \end{array}\right]\right\}
Dependent: Always Independent: Always

Studdy Solution
Analyze the conditions for dependence and independence:
- If a=0a = 0, the first vector becomes a scalar multiple of the second vector, leading to linear dependence. - If a≠0a \neq 0, check if the determinant of the matrix formed by the vectors is zero, indicating dependence.
The vectors are dependent when a=0a = 0 and independent otherwise. Therefore, the answer is: Dependent: a=0a = 0 Independent: a≠0a \neq 0

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