Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A. These may or may not be distinct. Show that det A = A₁ A2 A3. Make sure to submit a clear, complete, and detailed proof of this.
Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A. These may or may not be distinct. Show that det A = A₁ A2 A3. Make sure to submit a clear, complete, and detailed proof of this.
Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A. These may or may not be distinct. Show that det A = A₁ A2 A3. Make sure to submit a clear, complete, and detailed proof of this.
Please give a clear and complete solution. Linear algebra and differential equations
Transcribed Image Text:Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three eigenvalues of A.
These may or may not be distinct.
Show that det A = X₁ X₂ X3.
Make sure to submit a clear, complete, and detailed proof of this.
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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