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10 Nov 2019
Please give a detailed anwer!
Let Mnn be the set of all real n x n matrices, let 1 k, I n be fixed integers with k l, and let c 0 be a real number. Consider the function mu : Mnn rightarrow Mnn, whose image mu(A) for each A epsilon Mnn is defined by for To which elementary row operation does mu correspond? (No formal proof is required here, you can simply state your answer with a brief explanation.) Let E = mu(I). Prove that mu(A) = EA for every A epsilon Mnn. (Hint: Begin with the ij entry of EA and show that it equals the ij entry of fi(A), by using the definition of matrix multiplication and the definitions of E and mu(A).) (This proves one of the three cases implicit in Theorem 1.5.4 from the lectures.)
Please give a detailed anwer!
Let Mnn be the set of all real n x n matrices, let 1 k, I n be fixed integers with k l, and let c 0 be a real number. Consider the function mu : Mnn rightarrow Mnn, whose image mu(A) for each A epsilon Mnn is defined by for To which elementary row operation does mu correspond? (No formal proof is required here, you can simply state your answer with a brief explanation.) Let E = mu(I). Prove that mu(A) = EA for every A epsilon Mnn. (Hint: Begin with the ij entry of EA and show that it equals the ij entry of fi(A), by using the definition of matrix multiplication and the definitions of E and mu(A).) (This proves one of the three cases implicit in Theorem 1.5.4 from the lectures.)
Patrina SchowalterLv2
11 Feb 2019