Is the Determinant of Vectors A, B, and C Non-Zero for Linear Independence?

AI Thread Summary
The discussion focuses on proving that the vectors A, B, and C are linearly independent if and only if the determinant of their components is non-zero. The determinant is expressed as |(A1 A2 A3; B1 B2 B3; C1 C2 C3)|. Participants emphasize the importance of showing prior attempts to solve the problem before seeking assistance. The conversation highlights the necessity of including relevant equations and efforts in the initial post for effective help. Overall, the determinant's non-zero condition is crucial for establishing linear independence among the vectors.
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Show that a necessary and suffiecient condition that the vectors
A= A1i + A2j +A3k,
B=B1i + B2j + B3k,
C= C1i + C2j + C3k
be linearly independent is that the determinant |(A1&A2&A3@B1&B2&B3@C1&C2&C3)| be different from zero.
 
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What have you tried? Before you can get any help on this forum, you need to show some effort at solving this problem.

When you posted your question, you deleted the parts of the problem template that show relevant equations and what you have tried.
 

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