Help with Determinants [closed]

1. How do you split determinants?
2. What are the rules of determinants?
3. What is det 3A?
4. Can we add two determinants?

How do you split determinants?

Splitting of a determinant into sum of two or more determinants. If each elelment in any row or column, is sum of two terms, then the determinant can be expressed as the sum of two determinants.

What are the rules of determinants?

There are 10 main properties of determinants: reflection property, all-zero property, proportionality or repetition property, switching property, scalar multiple properties, sum property, invariance property, factor property, triangle property, and co-factor matrix property.

What is det 3A?

3A is the matrix obtained by multiplying each entry of A by 3. Thus, if A has row vectors a1, a2, and a3, 3A has row vectors 3a1, 3a2, and 3a3. Since multiplying a single row of a matrix A by a scalar r has the effect of multiplying the determinant of A by r, we obtain: det(3A)=3 · 3 · 3 det(A) = 27 · 2 = 54.

Can we add two determinants?

(vi) If elements of a row (or a column) in a determinant can be expressed as the sum of two or more elements, then the given determinant can be expressed as the sum of two or more determinants.