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9 Cards in this Set
- Front
- Back
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Does every matrix have a determinant?
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No, but every SQUARE matrix does.
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What is the determinant of a 1 x 1 matrix?
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Its single entry.
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What is the determinant of the square matrix: abcd?
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ad - bc
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If a matrix is named A, then the determinant of A is denoted:
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|A| or det(A). Does NOT mean absolute value.
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When using Cramer's rule for solving systems in two variables, what do D, Dᵪ, and Dᵧ represent?
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D = the coefficient matrix
Dᵪ = "c before b" Dᵧ = "a and c" |
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When using Cramer's rule for solving systems in two variables, x = ; y =
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x = Dᵪ / D
y = Dᵧ / D |
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What are the steps for using Cramer's rule to solve a system of linear equations in two variables?
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1) Put all the equations in standard form.
2) Set up the matrices, D, Dᵪ, and Dᵧ. 3) Find the determinants for D, Dᵪ, and Dᵧ. 4) Solve: x = Dᵪ / D ; y = Dᵧ / D |
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A matrix is not invertible IFF:
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its determinant = 0
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How can you easily tell if a matrix is invertible?
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Check its determinant. If the determinant is ZERO, it is NOT invertible.
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