Give an example of two vectors in R3 whose span is: a) a single point b) a line c) a plane
Give an example of two vectors in R3 whose span is: a) a single point b)...
Question 5: Multiple Choices Assume that vi,2,ig are vectors in R3. Let S span ,02,s and let A be the matrix whose columns are these vectors. Assume that 1 -1 1 0 0 0-3a +b-2c We can thus conclude that A. {6,6,6) is L1. B. The point (1,1 - 1) is in the span of (o,2,s) C. The nullity of A is 2 D. The rank of A is 3 E. B and C are both correct
Find vectors V1, ..., VKE R3 that span the plane in R3 with equation x-2y+32 = 0. How many do you need? Hint: Write down a parametrized solution for the equation.
(1 point) Select all of the vectors that are in the span of { ul , u2, u3 } . (Check every statement that is correct.) A. The vectoris in the span. 0 -3 B. The vector-52-7 2 is in the span C. The vector2 is in the span D. The vector -2 is in the span. E. All vectors in R3 are in the span. F The vector-70 is in the span. G. We cannot tell which vectors are...
Give an example of four nonzero vectors in R4 that do not span R4. explain
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2 The x-y plane Question 2 2 pts Describe the span of {(1,1,1),(-1,-1, -1), (2,2, 2)} in R3 A plane passing through the origin Aline passing through the origin R3 A plane not passing through the origin A line not passing through the origin Question 3 2 pts Let u and v be vectors in R™ Then U-v=v.u True False Question 4 2 pts Ifu.v...
(4) Find the span of the vectors You answer should be either: 0}, a 3 1 2 line through the origin, a plane through the origin, or R3. Determine which one it is. If it's a line or a plane, find its equation
5. Give an example of a basis for R3 which does not contain any of the vectors 00-0 and Justify your answer. 6. Show that {1, x - 1, (x - 1)2} spans P2 by showing that its span contains (1, x,x2}.
Differential Geometry:
1) Give an example of two vector fields X,Y E X(R3) such that for almost all p ER3 the three tangent vectors Xp, Yp, [X,Y] are a basis, but for some p they are not. However, at those special points p the three tangent vectors Xp, Yp, [X, [X,Y]]p form a basis. (Hint: The fields X and Y may span the Martinet distribution.) 2) Prove that any pair of vector fields X,Y with property 1) cannot be tangent...
2 2. Identify and Correct the Error. Describe geometrically the span of 5 -1/15] -1/6 in R3 1/10 Solution. The span of these two vectors is all the linear combinations of them, i.e. all 2 (-1/15) a 5 + b -1/6 1/10 for scalarsa, b. We have two vectors and two direction vectors span a plane. So the span of these two vectors is a plane with parametric equation: [-1/15) 5+t-1/6 with s,t real numbers. 1/10 BAD SOLUTION. The mistake...
Determine whether the set of vectors is a basis for R3. Given the set of vectors decide which of the following statements is true: A: Set is linearly independent and spans R3. Set is a basis for R3. B: Set is linearly independent but does not span R3. Set is not a basis for R3. C: Set spans R3 but is not linearly independent. Set is not a basis for R3. D: Set is not linearly independent and does not...