Lec 9 | MIT 18.06 Linear Algebra, Spring 2005

Lecture 9: Independence, Basis, and Dimension.

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Category:

Education

Tags:

• matrix theory
• linear algebra
• systems of equations
• vector spaces
• determinants
• eigenvalues
• similarity
• positive definite matrices
• least-squares approximations
• networks
• Fourier transforms
• Markov processes

[Lemnirot]

The second basis for R^3 is not a basis, since -(1,1,2)+2*(2,2,5)=(3,3,8); i.e., the vectors are not linearly independent.

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[stran1992]

If you guys find the determinant of the matrix, it shows Det = 1*(16-15) - 2*(8-6) + 3*(5-4) = 0. So the matrix is not linearly independent.

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[contactit]

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