MAT223H5 Study Guide - Midterm Guide: Augmented Matrix, Linear Combination, Elementary Matrix
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MAT223H5 Full Course Notes
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Document Summary
De(cid:12)nitions and concepts (you should be able to state/apply the de ni- tion/concept): Elementary row operations: (replacement) replace one row by itself plus a multiple of another, (interchange) interchange two rows, (scaling) multiply all entries in a row by a nonzero constant. Elementary row operations performed on the augmented matrix preserve the solution set. That is, spanfv1; : : : ; vpg is a collection of all vectors that can be written in the form c1v1 + c2v2 + : : : + cpvp with c1; : : : ; cp scalars. 375 = x1a1 + x2a2 + : : : + xnan. Ax = [a1 a2 : : : an] : : : + xnan = b which in turn has the same solution set as the system of linear equations whose augmented matrix is [a1 a2 : : : an b]. Rm be a transformation from rn to rm.
