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

[iric]

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.

 

[Mark44]

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