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Simultaneous
Linear Equations
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Cramer’s
rule (using the determinant) to solve systems of linear equations
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Solving system
of two equations in two unknowns using Cramer's rule
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Solving system of three equations
in three unknowns using Cramer's rule
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Method
of expanding a determinant of a rank n to cofactors |
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Cramer’s
rule (using the determinant) to solve systems of linear equations
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Solving system
of two equations in two unknowns
using
Cramer's rule
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A system of two equations in two unknowns, the solution to a system
by Cramer’s rule (use of determinants).
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the solution to the system |
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| Example:
Solve given system of
linear equations using
Cramer’s rule.
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Solving system of three equations in three unknowns
using
Cramer's rule
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A determinant of rank
n
can be evaluated by expanding to its cofactors of rank
n -
1, along any row or column taking into account the scheme of
the signs.
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| For example,
the determinant of rank
n = 3,
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| Example:
Solve given system of
three equations in three unknowns using method of expanding to
cofactors.
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Method of expanding
a determinant
of a rank n
to cofactors
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The value of a determinant will not change by adding multiples of
any column or row to any other column or row.
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This way created are zero entries that simplify subsequent calculations.
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Example:
An application of the method of expanding a determinant to
cofactors to evaluate the determinant
of the rank four.
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Added is third to the second colon. Then, the second row multiplied
by -3 is added to the first row. The obtained determinant is then
expanded to its cofactors along the second colon:
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The first colon multiplied by
-1 is added to the third colon. The
obtained determinant is then expanded along the third colon.
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| Intermediate
algebra contents |
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