Linear Algebra determinants

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12 Terms

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det(cA)

cndet(A)

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det⁡(Ak)

det⁡(A)k

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det(AB)

det(A)det(B)

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det(−A)

(−1)ndet(A)

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det(A-1)

1/det(A)

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How does row scaling affect determinant directly?

Multiplying one row by c multiplies det⁡(A) by c.

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How do row swaps affect determinant?

Swapping two rows multiplies the determinant by −1.

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How do row additions affect determinant?

Adding a multiple of one row to another leaves det⁡(A) unchanged.

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Shortcut: If a matrix is upper (or lower) triangular, what is its determinant?

The product of its diagonal entries.

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Similar matrices (A=PBP⁻¹)

Have the same determinant

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