Suppose that the set A ={X₁, X2..., Xn}, X₁ ER" spans the entire space R", i.e. for any arbitrary n -vector y E R",3 a set of coefficients {t₁, t₂,... tn} with at least one t; #0 such that 1tixi = y. Prove that the coefficients t₁, t₂,.., t are unique.

Q: Suppose v1, V2,..., Vm E V. Prove that {v1, v2, ..., Um} = (span(v1, v2, ..., Um))-.

A:

Q: -21 6. Find h so that the vectors 1 is in the span of the vectors 4, and -3 -0-

A:

Q: 4. For what value of h is vz in Span {v, v2} and for what value of h is {v1, V2, V3} linearly…

A: v1=1-32, v2=-39-6 and v3=5-7h

Q: (2) For every vector u and vector v in se A) True B False

A: Introduction: Vector is a quantity that has both magnitude and direction. Some mathematical…

Q: 1 -2 4 17. Let a 4 a2 -3 and b : For what 7 value(s) of h is b in the plane spanned by aj and a2?

A:

Q: 5. Label the following statements as true or false. If true, justify the statement. If false, give a…

A:

Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

A:

Q: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

A:

Q: 8. Let V={(x,y)x,y € R}. Define addition on V as follows: (x»x)+(x,y)=(x +2x, 1,y+Y,+2) Find the…

A: To find zero vector of V

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

A:

Q: Let S = {[x y z] | 3x + 2y + z = 0} . Write the set S as the span of a set of two vectors in R 3

A: Let (x,y,z)∈Sthen 3x+2y+z=0                          z=-3x-2yTherefore,…

Q: Consider the set V of all vectors of the form (x y 2) where x, y and z are real numbers 3. Show that…

A: