Give an example of four nonzero vectors in R4 that do not span R4. explain

Give an example of four nonzero vectors in R4 that do not span R4. explain
Give an example of two vectors in R3 whose span is: a) a single point b) a line c) a plane
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
3 Span Here is a list of four vectors: 1000 Is the vector 4 in the span the first four vectors? If it is, exhibit a linear combination of the first four 1-2 vectors which equals this vector, using as few vectors as possible in the linear combination.
Exercise 4.10.27 Here are some vectors in R4 21 r11 3 4 04 Thse vectors can't possibly be linearly independent. Tell why. Next obtain a linearly independent subset of these vectors which has the same span as these vectors. In other words, find a basis for the span of these vectors.
Write x as the sum of two vectors, one in Span (u1 "2."3) and one in Span (u4). Assume that(.,) is an orthogonal basis for R4
Write x as the sum of two vectors, one in Span {41,42,uz} and one in Span (14). Assume that (up ...,u4} is an orthogonal basis for R4. wale aume na mateso con una caranya yang masih san qay, Aune bat cu o sem mogen beste . 15 11 7 0 4 = 1 -6 lu=/7/ 1 , u, = -1 x=0 (Type an integer or simplified fraction for each matrix element.)
2. For each space below, give an example of a set that does not span the indicated space. Explain why (a) The subspace (lc d) a b) The subspace | y | | x + y + z = 0 R 2
#2
6.3.2 Question Help O Write v as the sum of two vectors, one in Span {41} and one in Span (42,43,44}. Assume that (47., U4} is an orthogonal basis for R4 1 1 1 4 4 -4 5 u1 u2 Uzi 44 -3 4 3 v= (Type an integer or simplified fraction for each matrix element.)
7. [4] Let S be the set of vectors in R4 (S [v,, v2,v3, v, v5)) where, v4 (-3,3,-9.-6) s (3, 9,7,-6) Find a subset of S that is a basis for the span(S).
Give an example of a linear combination of the vectors rs {(2). C), (47)} Give an example of a linear combination of the vectors from the previous problem that sums to be the zero vector (at least one coefficient must be non-zero).