MATH 235 Midterm: MATH 235 UMass Amherst practice-exam2-fall06-hints
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We see that this is a linear system with 3 equations in 3 unknowns. The matrix equation is a~x = ~b, where. Gaussian elimination to get the coe cient matrix in reduced echelon form. To solve this system, we form the augmented matrix . A vector ~v is in the kernel of a if a~v = ~0. 3 are x = 2 2t, y = 1 t, z = t or equivalently ~x = . Since there is no pivot in the third column, the third unknown is free and the solutions. 1: what does it mean for a vector to be in the kernel of a matrix a. 1: de ne what it means for a set s to be a basis of a subspace v rn. Give a set of vectors that span ker(a) and that are independent. A set of vectors s is a basis of v is v = span(s) and s is linearly independent.
