Let A= [r₁ , r₂] be a 2 × 2 matrix with rows r₁ and r₂ . If det(A)=5, find det(B). (a) Describe the properties and significance of the determinant in the context of linear algebra.
(b) Explain the process of finding the determinant of a 2 × 2 matrix and how it is related to the given matrix A.
(c) Discuss the transformation applied to A to obtain matrix B and how it influences the determinant.
(d) Utilize the determinant properties to find det(B) based on the information provided.