Question

Using properties of determinants find the determinant of the matrix A=2 B² if the determinant of B is known and equal to 5 . Let B be n × n matrix, then det(A)= det(2 B²)=2ⁿdet(B²)=2ⁿ·(det(B))²=2ⁿ· 5²=25 · 2ⁿ

Answer 1

The determinant of the matrix A = 2B² can be found by using properties of determinants. The determinant of A is equal to 25 · 2ⁿ, where n is the dimension of the matrix B.

Step-by-step explanation:

The determinant of the matrix A = 2B² can be found using properties of determinants. Let B be an n × n matrix, where the determinant of B is known and equal to 5. The determinant of A can be calculated as:

det(A) = det(2B²) = 2ⁿdet(B²) = 2ⁿ · (det(B))² = 2ⁿ · 5² = 25 · 2ⁿ