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A linear algebra question

asked 2022-12-21 15:35:26 +0100

tanyanlan gravatar image

updated 2023-05-19 21:51:21 +0100

FrédéricC gravatar image

Is it possible to solve this linear algebra question by SageMath?

Given column vectors v1=[1,1,3], v2=[1,0,-2] and v3=[a,3,3].

Question: for what value of a, the vector v3 is in the span of v1 and v2?

Thank you in advance.

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answered 2022-12-21 19:51:34 +0100

Max Alekseyev gravatar image

Determinant of the matrix formed by the given vectors must be zero, which gives an algebraic equation for a:

R.<a> = PolynomialRing(QQ)
v1=[1,1,3]
v2=[1,0,-2]
v3=[a,3,3]
eq = Matrix([v1,v2,v3]).det()
print(eq.roots(multiplicities=False))
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Asked: 2022-12-21 15:35:26 +0100

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Last updated: Dec 21 '22