Textbook Guide Mathematics: Linear Algebra And Its Applications, Indexed Family, Lincoln Near-Earth Asteroid Research
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Where b is a real or complex constant and the. The basic form of a linear equation is: (cid:1853)(cid:2869)(cid:1876)(cid:2869)+(cid:1853)(cid:2870)(cid:1876)(cid:2870)+(cid:1710)+(cid:1853)(cid:3041)(cid:1876)(cid:3041)=(cid:1854). n is any positive integer. Any equation that may be rearranged to the above form is a linear equation. A set of these equations involving the same variables is referred to as a system of linear equations which may have a solution in the form coefficients (cid:1853)(cid:3041) are real and complex. The subscript of a list ((cid:1871)(cid:2869), (cid:1871)(cid:2870), ,(cid:1871)(cid:3041)) that can be substituted for (cid:1876)(cid:2869), ,(cid:1876)(cid:3041) respectively. For example, the linear system: (cid:884)(cid:1876)(cid:2869) (cid:1876)(cid:2870)+(cid:883). (cid:887)(cid:1876)(cid:2871)= (cid:890) (cid:1876)(cid:2869) (cid:886)(cid:1876)(cid:2871)= (cid:889) Has the solution list (5, 6. 5, 3), which when substituted back into the linear system for (cid:1876)(cid:2869),(cid:1876)(cid:2870),(cid:1876)(cid:2871) results in a simplification of the two equations to 8 = 8 and -7 = -7. The solution set is the set of all possible solutions of a linear system and two linear systems are equivalent if they have the same solution set.
