MATH 2211 Midterm: AnsQ2mt210
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Determine if b is a linear combination of a1, a2 and a3. If it is, nd the weights c1, c2, c3 so that c1a1 + c2a2 + c3a3 = b. We need to determine if the vector equation x1a1 + x2a2 + x3a3 = b has a solution. We consider the augmented matrix [a1 a2 a3 b] and nd its reduced echelon form. General solution = c1 = 2 5c3, c2 = 3 4c3, c3 is f ree. Since the vector equation has a solution, b can be written as a linear combi- nation of a1, a2 and a3. For example, if c3 = 0, then c2 = 3 and c1 = 2.
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