Is the following set of vectors from P^3 linearly independent? Give reasons.
[1], [1+2x+3x^2], [1+3x^2]
2026-04-18 22:55:41.1776552941
Linear independence, linear analysis
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Whatever linear combination of the three polynomials you form, the $x$ term cannot be cancelled out unless the coefficient of the second polynomial is zero. Then whatever linear combination of the remaining two polynomials you form, the $x^2$ cannot be cancelled out unless the coefficient of the last polynomial is zero.