computing and properties of determinants

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11 Terms

1
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upper triangular matrix

all entries below diagonal are zero

2
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lower triangular matrix

all entries above diagonal are zero

3
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suppose A → B with one ERO
if ERO was Ri → cRi

det(B) = cdet(A)

4
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if ERO was Ri → Ri + cRj

det(B) = det(A)

5
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if ERO was Ri ←> Rj

det(B) = -det(A)

6
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if A is upper or lower triangular, then det (A) =

a11 a22 a33 … ann

7
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det (I) =

1

8
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if A has a zero row or column, then det (A) =

0

9
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if A has two identical rows or columns, then det(A) =

0

10
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if A is n x n, det (cA) =

cndet(A)

11
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if A has block - triangular form, then det (A) =

det(B1)det(B2)