Math II
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FlashcardsWhat is a linear system (LS)?
A set of m linear equations in n variables.
When is a linear system homogeneous?
When all constant terms b₁,b₂,...,bₘ=0
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14 Terms
What is a linear system (LS)?
A set of m linear equations in n variables.
When is a linear system homogeneous?
When all constant terms b₁,b₂,...,bₘ=0
What are the elementary row operations used in Gaussian Elimination?
(1) Swap rows, (2) Multiply a row by a nonzero scalar, (3) Add a multiple of one row to another.
What are the possible types of solutions to a linear system?
(1) No solution, (2) One solution, (3) Infinitely many solutions.
What is the augmented coefficient matrix?
The coefficient matrix with an extra column for the constant terms
What makes a solution a "trivial solution"?
All variables equal zero.
When is a set of vectors linearly independent?
When no vector in the set is a linear combination of the others.