4. Prove that if A is diagonalizable and has eigenvalues λ₁, A2, .. An, then the determinant of A is the product of its eigenvalues: |A| = A₁ A2 ···• An.
4. Prove that if A is diagonalizable and has eigenvalues λ₁, A2, .. An, then the determinant of A is the product of its eigenvalues: |A| = A₁ A2 ···• An.
4. Prove that if A is diagonalizable and has eigenvalues λ₁, A2, .. An, then the determinant of A is the product of its eigenvalues: |A| = A₁ A2 ···• An.
Transcribed Image Text:4. Prove that if A is diagonalizable and has eigenvalues A₁, A2, ..., An, then the determinant of A is the
product of its eigenvalues: |A| = A1 A2 · · · An·
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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