# Linear Algebra with Applications

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Name: ANSWER KEY Math 20F - Linear Algebra - Winter 2003 Quiz #1 — January 14 1. Consider the following system of linear equations: x 1 x 2 + 3 x 3 + 4 x 4 = 5 x 2 x 4 = 6 . Is the system consistent? YES Is the system underdetermined? YES Is the system overdetermined? NO Is the system homogeneous? NO What is its solution set? ANSWER: Set x 3 = α , x 4 = β . Solution set = { (11 3 α 3 β, 6 + β, α, β ) : α, β R } . 2. Consider the matrix A = 1 2 3 4 1 3 3 6 1 3 1 0 . Express A in reduced row echelon form (rref). Show your work; use the
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