THIS PART OF THE WRITING ASSIGNMENT IS TO BE COMPLETED IN PEERSCHOLAR, IN THREE PHASES: CREATE, ASSESS, AND REFLECT. IN THE CREATE PHASE, DRAFT A NEAT (COHERENT & LEGIBLE, PREFERABLY TYPESET) RESPONSE TO THIS PART OF THE WRITING ASSIGNMENT (AND THIS PART ONLY) AND UPLOAD YOUR DRAFT TO PEERSCHOLAR. IN THE ASSESS PHASE, EXCHANGE ANONYMOUS FEEDBACK ON YOUR CREATIONS. BEFORE PROCEEDING TO THE REFLECT PHASE, ASSESS YOUR OWN ORIGINAL SUBMISSION. IN THE REFLECT PHASE, REVISE YOUR SUBMISSION, AND UPLOAD A FINAL COPY. Slodowy and Nakajima are arguing about the following claim: EiP where each Ei is an elementary Any square matrix can be written as a product Ex: matrix and P is the matrix for a projection. Slodowy thinks: The claim is true because elementary matrices are the same as row reduction. Nakajima is not yet convinced: I see that the determinant of a square matrix is going to be the determinant of such a product, but I don't see why the matrix itself has to be such a product. Explain to Slodowy and Nakajima, using complete sentences, whether or not the claim true. (i) Fill out the details of Slodowy's argument, or show that the claim is false and explain where Slodowy's argument went wrong. (ii) Fill out the details of Nakajima's observation, or show that it is not true by giving a counterexample. THIS PART OF THE WRITING ASSIGNMENT IS TO BE COMPLETED IN PEERSCHOLAR, IN THREE PHASES: CREATE, ASSESS, AND REFLECT. IN THE CREATE PHASE, DRAFT A NEAT (COHERENT & LEGIBLE, PREFERABLY TYPESET) RESPONSE TO THIS PART OF THE WRITING ASSIGNMENT (AND THIS PART ONLY) AND UPLOAD YOUR DRAFT TO PEERSCHOLAR. IN THE ASSESS PHASE, EXCHANGE ANONYMOUS FEEDBACK ON YOUR CREATIONS. BEFORE PROCEEDING TO THE REFLECT PHASE, ASSESS YOUR OWN ORIGINAL SUBMISSION. IN THE REFLECT PHASE, REVISE YOUR SUBMISSION, AND UPLOAD A FINAL COPY. Slodowy and Nakajima are arguing about the following claim: EiP where each Ei is an elementary Any square matrix can be written as a product Ex: matrix and P is the matrix for a projection. Slodowy thinks: The claim is true because elementary matrices are the same as row reduction. Nakajima is not yet convinced: I see that the determinant of a square matrix is going to be the determinant of such a product, but I don't see why the matrix itself has to be such a product. Explain to Slodowy and Nakajima, using complete sentences, whether or not the claim true. (i) Fill out the details of Slodowy's argument, or show that the claim is false and explain where Slodowy's argument went wrong. (ii) Fill out the details of Nakajima's observation, or show that it is not true by giving a counterexample