-2 bị b2 ,and W = Span {uj, U2}. Let uj 4 u2 = -5 b3 Find an implicit description of W ; that is, find a set of one or more homogeneous equations that characterize the points of w. [Hint: When is b in W?

Q: 12 3. 5. 13 18 -1 For what value of hs in the plane spanned by j and i? Preview Answers Submit…

A:

Q: Let 6. 21 2 V2 = 4 9 For what value of h is y in the plane spanned by vj and v2? h =

A:

Q: ow that c=3i -2j1+k and d=2j+ 4k are orthogonal.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: (a) a = (2, 6, 0) , b = (4, –1, 1) (b) a =i-j-k, b = }i+j- 4k

A: a) given that  a=<2,6,0> , b=<4,-1,1> a→=2i+6j+0kb→=4i-j+ka→×b→=ijk2604-11…

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

A:

Q: Find the length and direction (when defined) of u x v and vxu. u= 5i + 3j – 5k, v=0

A: we know that  uxv=|u|.|v|sin∅.n^where ∅ is angle between u and v and n^ is unit vector perpendicular…

Q: Find whether the planes below intersect, and if so, where they intersect using Gaussian elimination.…

A:

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j. Find the specified scalar u . v + u . w

A:

Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: 4- The direction cosines of are: -1 a) -1 3 b) J14 V14 V14 2 -3 -3 2 c) 14 14 14 2 -1 3 d) 14' 14 14…

A:

Q: Find the length and direction (when defined) of u x v and vxu. u= - 12i + 9j – 12k, v = - 4i + 3j –…

A: Using formula of u x v and v x u,

Q: Evaluate S. F·dr, if S'is the portion of the paraboloid z = 4 – x² – y² for which z 2 0 and F(x, y,…

A:

Q: Prove that the planes determined by the equations ax + by + c z = d and αx + β y + γ z = δ are…

A: Given planes, ax + by + c z = d αx + β y + γ z = δ

Q: Prove that if T:V-oW io a one to-one linear trans formation and 33 o a linearly deperdent then…

A:

Q: M 13. Are points J, K, and L collinear? 14. Are points J, K, and L coplanar? 15. Are points J, K,…

A: Since you have asked multiple question, we will solve the first 3.question for you as per our guide…

Q: 2. Consider a natural cubic spline model with two knots at ci and c2 given by y = Bo + B1r+ B2(r -…

A: Given, spline model, y=β0+β1x+β2x-c13+β3x-c33+∈                         β2+β3=0  ,  β2c1+β3c2=0…

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j.Find specified scalar u . v + u . w.

A: Given: u=2i-j, v=3i+j & w=i+4j To find: u·v+u·w

Q: R lies between J and W on JW. Given that JR: RW = 3:4, R = (-5,1), and W = (6,8), find the…

A: Given that point R lies between J and W , JWJR:RW=3:4 and R-5,1 , W 6,8 Solution : let J…

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). %3D %3D = (0, 6) V = a b…

A:

Q: Let u = 10i + 2j, v=i+j, and w = i-j. Find scalars a and b such that u = av + bw. a = b =

A:

Q: Given v = - 7i + 5j and w= -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

A:

Q: Find a basis for the set of vectors in ℝ3 in the plane × + 2y + z = 0. [Hint: Think of the equation…

A:

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j.Find specified scalar 4(u . v).

A: it is given that, u = 2i - j, v = 3i + j, and w = i + 4j

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j. Find the specified scalar 4(u.v)

A: Given that u = 2i - j,   v = 3i + j  and  w = i + 4j. Obtain 4u·v as follows.

Q: 7. If a =i+ 3j – k, b= 2i+ 4j – 2k and c = -i+2j+ 4k, find a number A such that d= a+b+ Ac is…

A: Given a=i+3j-k b=2i+4j-2k c= -i+2j+4k Find the  λ such that d= a+b+λc is parallel to the yz plane…

Q: 24. The value of the constant 2, for which the plane Ax – 3y + 4z = 5 and the line r = i- 2j – 3k +…

A:

Q: n (c) Find a vector b in R³ such that the solution set of Ax = b is a line in R³ parallel to the…

A: Introduction: Only when there is a 0 degree angle between two vectors can it be said that they are…

Q: Find the length and direction (when defined) of u xv and vxu. u= - 12i + 8j – 20k, v = - 3i + 2j -…

A: To find the length and direction of u→×v→, first find the value of u→×v→ by cross product. The given…

Q: If a = i+3j – k, b = 2i + 4j – 2k and c = -i + 2j +4k, find a number A such that d = a +b+ Xc is…

A:

Q: A solid figure projects the same shape on the x-y, y-z, and x-z view. Which of the following…

A: A solid object have same shape on x-y, y-z and x-z view.

Q: Let 3 6. 6. 4 11 j = 14 For what value of h is y in the plane spanned by vị and v2? h =

A:

Q: 1 7 Let a, 4 21 and b = 6. 1 2

A: here we can use matrix method to write the equation of plane and then we use the condition that b…

Q: Let u = i - 2j, v = 2i + 3j, and w = i + j. Write u = u1 + u2, where u1 is parallel to v and u2 is…

A: u1 is parallel to v and u2 is parallel to w.So u1= av and u2=bwWhere a and b are constants.

Q: Find the component of u along v. u = 31 - 24j, v =j

A: component of vecor u along vector v is=u→.v→v→givenu=3i-24jv=j

Q: Let u = 2i + j, v = i + j, and w = i - j. Find scalars a and b such that u = av +bw.

A: Given u = 2i + j, v = i + j, and w = i - j.Plug them in the equation u = av +bw.

Q: Given that the vectors X and X2 are solutions of a system -X = AX, find the Wronskian and determine…

A: For X1,X2, Solutions of dXdt=AXW(X1,X2)=det(X1,X2)If  W(X1,X2) is nowhere zero Then the solutions…

Q: Let a = 4i + 3j – k, b = 2i – j + xk and c = yi + zj – 2k. Find: %3D %3D a x such that a and b are…

A: Two vectors are said to be perpendicular to each other if their dot product is zero. We will use…

Q: Find i x w if ||T|| = 3, ||w|| = 4, 0 = and ī, w both lie in the xz-plane (as shown). 3 %3D

A:

Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

A: (a) To show that triangle ABC is a right angled triangle, use scalar product of vector, that is…

Q: Find a set of vectors {u°, v*} in R4 that spans the solution set of the equations w-x-2y+3z=0…

A:

Q: Let u = 8i + 2j, v=i+j, and w =i-j. Find scalars a and b such that u = av + bw. a = b =

A:

Q: 98 25) Gvon vectors v= 30tj and w=-2i -j. Decompose v into two vectors V, and Vz, where V, is…

A:

Q: Let u = 2i - j, v = 4i + j, and w = i + 7j. Find the specified scalar. u•v+u•w +u•w= (Simplify your…

A:

Q: Let u = 6i + 2j, v =i+j, and w =i-j. Find scalars a and b such that u = av + bw. a = b =

A:

Q: Find whether the planes below intersect, and if so, where they intersect using Gaussian elimination.…

A: we first solve the augmented matrix and get the parametric equation of a line using the guassian…

Q: Let u = 2i - j, v = 4i + j, and w = i + 7j. Find the specified scalar. u•v+u•w

A:

Q: Let T: M2x2(R) → M2×2(R) be defined by T(A) = A 2 1 1 %3D Is T diagonalizable? Show work and…

A:

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v (0, 24) %3D a =…

A:

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: Show that u and v are perpendicular in each of the following cases. (i) u = 31 -j+ 2k , v= 2i + 5j –…

A: