Find a basis for the given subspace by deleting linearly dependent vectors. Very little computation should...
(1 point) Find a basis of the given subspace by deleting linearly dependent vectors. span of 0, 0 LoJ LO 0 0 A basis is
Use the solution method from this example to find a basis for the given subspace. 1 4 0 5 1 S = span -1 0 -1 4 0 5 Give the dimension of the basis.
Please answer questions 2&3. Thank you! Remember that: A subspace is never empty, and is either the just the zero vector. i.e. [0), or has an infinite number of vectors A basis for a subspace is a set of t vectors. where t is the dimension of the subspace (usually a small number.) These vectors span the subspace and are linearly independent. This means that 0 can never part of a basis. The basis of the subspace (0) is empty....
3. Show, by inspection (without forming a matrix), that the given vectors are linearly dependent. vi = (1, -1,0,1), v2 = (1,1,1,0), 3 = (1,2,0,1), 74 = (-1, -2, 1,0) 2 -1 ::: - سه 4. Let S = 6 3 Is S a basis for R?? Explain your answer. 0 0
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly dependent? c. What is the angle (in degrees) between u and v? 4. Here are two vectors in R". Let V = the span of {"v1r2} a. Find an orthogonal basis for V (the orthogonal complement of V). b. Find a vector that is neither...
7. In each part of this problem a set of n vectors denoted V, , denoted V. Carefully follow these directions V, is given in a vector space i) Determine whether or not the n vectors are linearly independent. i) Determine whether or not the n vectors are a spanning set of V Then find a basis and the dimension of the subspace of V which is spanned by these n vectors. (This subspace may be V itself.) a. V...
Determine whether the given set of vectors is linearly dependent or linearly independent. U1 = (1, 2, 3), u2 = (1, 0, 1), uz = (1, -1, 5) linear dependent linear independent
Let W be the subspace spanned by the given vectors. Find a basis for Wt, 0 1 A. W1 = W2 = 3 2 -1 2 B. W W2 2 -3 W3 = 6
(1 point) Find a linearly independent set of vectors that spans the same subspace of R3 as that spanne -3 3 3 2 -5 -2 4 0 Linearly independent set:
Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. The value(s) of h which makes the vectors linearly dependent is(are) 188 because this will cause (Use a comma to separate answers as needed.) x3 to be a free variable