MAT223H1 Study Guide - Midterm Guide: Additive Inverse, Scalar Multiplication, Gaussian Elimination
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October 25, 2007: bachurin, a. fischer, b. koenig, s. uppal. [4] 1(a) every homogeneous system of 4 linear equations in 6 unknowns has a solution. true false. A system of 4 linear equations will have at most 4 leading ones, and since there are. 6 unknowns and the system is homogeneous the set of solutions requires at least 2 parameters. Therefore, there are in nitely many solutions to the system. [4] 1(b) it is impossible for a system of linear equations to have exactly two solutions. true false. Every solution to a system of equations ax = b is of the form x = xp + x0 where. Xp is a particular solution to ax = b and x0 is a solution to ax = 0. X2 are two solutions to ax = 0, so is x1 + x2 (the set of solutions to a homogeneous system of equations is a subspace).
