(5) Let V=R2. For (1, 1), (2, 32) EV and c ER, define addition and scalar multiplication operations by (T1, y₁) (2, 2) = (1 + 2x2, y₁ + 3y2), (0,0) if c = 0, (cr₁, ) if c# 0. Is (V,0,0) a vector space over R? If No, please mention each axiom which is not satisfied by these operations. co (1.1):

Q: Please show me the steps to solve this question. It is a part of vector calculus.

A: Value of the integral is 9/16Explanation:

Q: Let V=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ +…

A:

Q: Do only question 6

A: Evaluate fx​(3,1)Evaluate fy​(3,1)Find the derivative of f(x,y) with respect to x, treating y as a…

Q: What is the dimension of the vector space M,x3R)?

A: SOLUTION-

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

A:

Q: Set V = {(x, y) | x ER, YER}. Define addition of vectors by the rule (x, y) + (x, y) = (y + y',x+x')…

A:

Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: Do question 12 only

A: The given in item #12 is:∫04π​​∫01​∫0x2​xcos(y) dz dx dy Consider the innermost…

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: Do only question 5

A: Step 1:Identify the variable you're differentiating with respect to. Let's say you want to find…

Q: If V is vector space, with u = (u, , U2) and v = (v, , v2) with u +v = (u,+v, , u2+v2) and ku =…

A: u=(u1,u2) , ku=(3u1,0) k=2, u=(-1,2)

Q: (×q) × (gxv) + (gxg) x (xv) + (x) x (qxv)

A:

Q: The linear operator L : R² R² given by L (²) 6x - a) (55x + y) = -1 Which of the following gives a…

A:

Q: Do only question 7

A: To find the equation of the plane that is tangent to the given surface at a specific point, we need…

Q: If V₁, V2 and v3 are 3 vectors in a vector space V such that -7v₁-9v2 = 0. V, and v₂ are linearly…

A: Given that v1, v2, and v3 are 3 vectors in a vector space Vsuch that -7v1-9v2=0. Then v1, v2,and v3…

Q: If vectors b, c and d are not coplanc then prove that vector

A:

Q: Let (V, (, )) be an inner product space and let v, w be vectors in V. If (v, w) = 7 and w = 5, then…

A:

Q: 6. Let V be the vector space of all diagonal 5 x 5 matrices, then dim(V)=--

A: Given that the vector space contains all diagonal 5×5 matrices and we need to find its dimension.

Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (x, , y.) +…

A: We have to show that the set V with the addition operation x1, y1+x2, y2=x13+x233, y13+y233 and…

Q: Do question 10 only

A:

Q: r- {{: :] T = " E M22| a = - dis a vector space under standard matrix addition and scalar…

A: I have proved T is a subspace

Q: Do only question 8

A: To find the equation of the plane tangent to the surface  f(x,y)=x+yx​ at the point (1, 2), we need…

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: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

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

A:

Q: Do only question 4

A: Questio(4)Part(a)Find limt→∞​r(t):Given r(t)=⟨2sin(t),3cos(t),t2⟩, as t→∞,sin(t) and cos(t)…

Q: Do question 9 only

A: Step 1: Compute the Gradient of 𝑓Given f(x,y)=x2ey,Compute the partial…

Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (7, , v.) +…

A:

Q: Let B' = {u1,u2} and ß = {v1,v2} be ordered bases for a 2-dimensional vector space V. Given that [u1…

A: Given u1+u2β=5,4t, and the change of coordinate matrix Q from β' to β is Q=1c3d. Express v1 as a…

Q: {{::) eR}. sider V = : #1, 22, 23 > 0 and ¤1, x2, x3 ER pose the vector addition and scalar…

A:

Q: →→→ Let x, y, z be vectors such that x X X y x z →→ = a; y x ➜>> Z X X y = b and ° {(+5) x = -(-+)}…

A: It is given that x→=y→=z→=2 x→,y→,z→  makes angle of 600 with each other.x→×y→×z→=a →  ; y→×z→×x→=b→…

Q: d). Let K = {(x;y) | x,y e R} with operations (x1;y1) (X2;y2) = (x, + x2 + 1; y, +y2 - 2) %3! (ax, +…

A: Given: K=x;y | x, y∈ℝ with operations x1, y1⊕x2, y2=x1+x2+1; y1+y2-2 and a⊗x1;y1=ax1+a-1; ay1-2a+2.…