MATH 2211 Quiz: Quiz2mt210Sample2Ans
Document Summary
Is b = and a3 = . 1. vector equations a linear combination of the vectors a1 = . To answer this question, we need to solve the vector equation x1a1 + x2a2 + x3a3 = b. In other words, we need to reduce the augmented matrix [a1 a2 a3 b]. Note that the last augmented matrix corresponds to an inconsistent system. Therefore, the vector equation x1a1 + x2a2 + x3a3 = b has no solution which means that b is not a linear combination of a1, a2 and a3. To answer this question, we need to solve the vector equation x1v1 + x2v2 = y. In other words, we need to reduce the augmented matrix [v1 v2 y]. Since we want y span{v1, v2}, we need a consistent system. Therefore, we have to have 7 + 2h = 0. In other words, y is in the plane generated by v1 and v2 when h = 7/2.
