Test 1 study guide

Test 1 study guide - Elementary Row Operations: 1....

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1. Interchange two rows 2. Multiply a row by a nonzero real number 3. Replace a row by its sum with a multiple of another row Over-determined System : More equations than unknowns. In R 2 each equation represents a line, usually inconsistent. Underdetermined System: A system with fewer equations than unknowns. Usually consistent with infinitely many solutions. Inconsistent System: A system with no solutions. Consistent System: A system with one or infinitely many solutions. Reduced Row Echelon Form: 1. If the first nonzero entry in each nonzero row is 1. 2. If row k does not consists entirely of zeros, the number of leading zero entries in row k+1 is greater than the number of leading zero entries in row k. 3. If there are rows whose entries are all zero, they are below the rows having nonzero entries. Matrix-vector multiplication : If A is an mxn matrix and x is a vector in R n then Ax = x 1 a 1 + x 2 a 2 + … + x n a n Consistency Theorem: A linear system Ax=b is consistent if and only if b can be written as a linear combination of the column vectors of A. Matrix-Matrix Multiplication:
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Test 1 study guide - Elementary Row Operations: 1....

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