Question

6. Consider the following set of vectors: v1 = [-1, 1, -2], v2 = [3, 3, 6], v3 = [9, 0, 0]. (a) Show that, all the vectors are linearly independent. (b) Do the vectors, v1 and v2 span R^3? Justify your answer. (c) Do the vectors, v1, v2, and v3 span R^3? Justify your answer. (d) Is the set of vectors {v1, v2, v3} can be a basis of R^3? 7. Determine the dimension of the solution space of the system Ax = 0. Also, show the parametric representations of the solution space. (a) [2 0 3; 3 2 0; 8 4 3] (b) [2 2 -4; 4 4 -8; -1 -1 2]

          6. Consider the following set of vectors:
v1 = [-1, 1, -2], v2 = [3, 3, 6], v3 = [9, 0, 0].
(a) Show that, all the vectors are linearly independent.
(b) Do the vectors, v1 and v2 span R^3? Justify your answer.
(c) Do the vectors, v1, v2, and v3 span R^3? Justify your answer.
(d) Is the set of vectors {v1, v2, v3} can be a basis of R^3?
7. Determine the dimension of the solution space of the system Ax = 0. Also, show the parametric representations of the solution space.
(a) [2 0 3; 3 2 0; 8 4 3]
(b) [2 2 -4; 4 4 -8; -1 -1 2]

6. Consider the following set of vectors:
v1 = [-1, 1, -2], v2 = [3, 3, 6], v3 = [9, 0, 0].
(a) Show that, all the vectors are linearly independent.
(b) Do the vectors, v1 and v2 span R^3? Justify your answer.
(c) Do the vectors, v1, v2, and v3 span R^3? Justify your answer.
(d) Is the set of vectors v1, v2, v3 can be a basis of R^3?
7. Determine the dimension of the solution space of the system Ax = 0. Also, show the parametric representations of the solution space.
(a) [2 0 3; 3 2 0; 8 4 3]
(b) [2 2 -4; 4 4 -8; -1 -1 2]

Added by Veronica B.

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