Question Number :1 Correct :1 Wrong : 0 Consider the vector space V = {a, + a,x+a,x²:a, eR for i = 0,1.2) of polymomials of degree at most 2. Let f:V-→R be a linear functional such that f(1+x)=0, f(l-x')=0 and f(x? -x)=2. Then f(l+x+x°) equals

Q: The set of vectors in R? with y = -3x is a real vector space

A:

Q: Let V = R². For (u₁, U2), (v₁, v₂) € V and a ER define vector addition by (u₁, U₂) (V1₁, V₂) = = (U₁…

A:

Q: Determine whether the vector functions, x1(t)= [ et ]           [ -et ] and x2(t)= [ et ]…

A:

Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: Let L be the line in R³ that consists of all scalar multiples of the vector onto L. proje 22 T .…

A:

Q: With T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: The given matrix  and the vector  and  is defined by .The aim is to find the vector  whose image…

Q: Ollowing fünctión. T: R2 R2, T(x, y) = (x, 8) Find the following images for vectors u = (u,, u,) and…

A:

Q: Let V be the vector space of functions spanned by B = {bị = 6 sin æ + 4 cos a, b2 = 2 sin æ + 7 cos…

A:

Q: Let v=(1', 1, 3.), u=(0, -4', 1) are nonzero vectors in R³. Subtask (a). Whether a linear functional…

A: Functional Analysis:

Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: Let S be the space of all complex vectors (x, y, z) such that y = z². Determine whether or not S is…

A: In the given problem we verify the properties of vector addition

Q: Can duality principles be related to the concept of orthogonality in vector spaces?

A: The duality principle is a concept that appears in various branches of mathematics and physics. It…

Q: HIf vectors x, y, z, u in the real vector space p (the polynomials) are defined by x(t)=1, y (t)=t,…

A:

Q: In P2 (polynomials of degree s2), let v =1+x+2x, v, = 3- 2x +x', Determine whether the vector v…

A: Let's find.

Q: 1. 3) Suppose A = 4i-6j, B = i + 7j and C = 9i - 5j. Find (a) ||5B-3C|| (b) unit vector having the…

A:

Q: Let V = R' and define vector addition as (x, y, z)+(x', y', z')= (x+x',y+y',z+z') (standard…

A:

Q: 3c

A: Step 1:a) To evaluate the adjoint (or conjugate transpose) of the linear operator T on the inner…

Q: H.W: Let V = {(x, y): x 20} with standard operation on R2. Is Va vector space?

A:

Q: Let $K$ is a horizontal shear, next draw a vector $\vec{x}=\left[\begin{array}{l}x_1 \\…

A: Let be the transfomation representing vertical shear of the vector  .Then we have The above can be…

Q: 4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ =…

A:

Q: are vectors in R³ are linearly independent but ü,v,w are linear dependent. Show that there exist…

A:

Q: 49. Show that in the vector space V, (R), the vectors (1, 2, 3), (- 2, 1, 4), (- 1, – 1/2, 0) form a…

A: We prove that the set of vectors form a linearly dependent set.