MATH 1025 Lecture Notes - Augmented Matrix, Matrix Addition, Gaussian Elimination
11 Apr 2023
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Class 5: rank, matrix addition, scalar multiplication, transposes. The rank of a (coe cient) matrix a, denoted rank(a) is equal to In classes 3 and 4, we used row reduction to solve several systems of equations. The augmented matrices (in rref) of these systems are shown on the left below. Rank of coefficient x = 23 y = 6 z = 3. For consistent systems, i. e. systems with at least one solution, we can see that: where a is the coe cient matrix for the system. This is always true for homogeneous systems since Write the solutions to the original system of equations in parametric form (i. e. using param- eters r, s, t, etc. ). Options: (a) 1 parameter (b) 2 parameters (c) 3 parameters (d) no parameters. So far, we have seen augmented matrices and coe cient matrices. In general, a matrix is simply a rectangular array of numbers, e. g. 2.
