For each of the following sets of vectors, decide whether the set is linearly dependent or
linearly independent. You should justify your answers completely. For those sets that are
linearly dependent, write one of the vectors as a linear combination of the others.
(a) {(1; 2; 3; 2); (2; 5; 5; 5); (2; 6; 4; 6)}.
(b) {(1; 1; 3; 4); (0; 2; 3; 1); (4; 0; 0; 2)}.
(c) {(0; 1; 1;-1); (k; 1; 1; 0); (1; 3; 3;-2)} (and how does the answer depend on k element of R?).
Don't we have to arrange the vectors in columns rather than rows? I asked this question before and expert answered with vectors in rows but theorem we have been taught says vectors must be arranged in columns and reduced to reo echelon form and then get rank to determin whether dependent or independent.
For each of the following sets of vectors, decide whether the set is linearly dependent or
linearly independent. You should justify your answers completely. For those sets that are
linearly dependent, write one of the vectors as a linear combination of the others.
(a) {(1; 2; 3; 2); (2; 5; 5; 5); (2; 6; 4; 6)}.
(b) {(1; 1; 3; 4); (0; 2; 3; 1); (4; 0; 0; 2)}.
(c) {(0; 1; 1;-1); (k; 1; 1; 0); (1; 3; 3;-2)} (and how does the answer depend on k element of R?).
Don't we have to arrange the vectors in columns rather than rows? I asked this question before and expert answered with vectors in rows but theorem we have been taught says vectors must be arranged in columns and reduced to reo echelon form and then get rank to determin whether dependent or independent.
