Linear Algebra Examples

Solve Using a Matrix with Cramer's Rule
,
Represent the system of equations in matrix format.
The determinant of is .
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These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by .
Multiply by .
Add and .
The determinant of is .
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These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by .
Multiply by .
Add and .
The determinant of is .
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These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by .
Multiply by .
Add and .
Find the value of by Cramer's Rule, which states that . In this case, .
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Remove parentheses.
Move the negative in front of the fraction.
Find the value of by Cramer's Rule, which states that . In this case, .
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Remove parentheses.
Move the negative in front of the fraction.
The solution to the system of equations using Cramer's Rule.
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