Flashcards
Lin Al
Cards in this deck (11)
- 1A linear equation in n unknowns is an equation of the form
- 2m × n linear systemA linear
system of m equations in n unknowns
- 3If a linear system has no solution, it is calledinconsistent
- 4If the system has at least one solution, it is calledconsistent
- 5The set of all solutions of a linear systemsolution set
- 6If it is consistent, it must have either ___ many solutions (3)exactly one or infinitely
many solutions - 7When are two systems of equations involving the same variables equivalentthey have the same solution set
- 8The three operations that can be used on a system to obtain an equivalent systemI. The order in which any two equations are written may be interchanged.
II. Both sides of an equation may be multiplied by the same nonzero real number.
III. A multiple of one equation may be added to (or subtracted from) another. - 9Requirements for system to be in strict triangular formIn the kth equation, the coefficients of the first k − 1 variables are all zero and the coefficient of x k is nonzero
(k = 1, . . . , n).
{As long as the main diagonal is filled w/ anything except ZEROS} - 10method of solving a strictly triangular system where first, the nth equation is solved for the value of x_n which is used to solve the (n − 1)st equation and so on.back substitution
- 11array of numbers whose entries are the coefficients of the Xi ’s
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- Flashcards on Lin Al, created by Spam neverread on 09/03/2024.
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- Spam neverread
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