Which of the following sets are subspaces of R? OA. {(-2, y, z) | y, z arbitrary numbers } B. {(x, y, z) | x + y+z = -5} OC. {(x, y, z) | 2x – 6y = 0, 9x + 5z = 0}

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

A:

Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

A:

Q: Let S be the parallelogram determined by the vectors b₁ S under the mapping x+Ax. 3 = and b₂ ---H -6…

A:

Q: IP IE Express the vector + =[] y as a linear combination of = [2] -[1] and y=

A:

Q: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: et S be the subspace of IR° spanned by u and v. Find the closest vector p in S to the vector w. -2 7…

A: In this question, concept of basis is applied. Basis A basis for a vector space V is a collection of…

Q: EXER 3.2 - LINEAR ALGEBRA Write v =(4,4,5) as a linear combination of x=(1,2,3), y =(-2,0,1) and z =…

A:

Q: as a linear combination of x = 7 4 and y = -3 Express the vector u -2

A: NOTE: Refresh your page if you can't see any equations. . write both vectors x and y in the matrix…

Q: Find the closest point to y in the subspace W spanned by v₁ and v2. y= 3 -1 1 16 V1 11 1 -4 1 5 V2 =…

A:

Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: What restrictions must be made on x, y, and z so that the triple (x, y, z) will represent points on…

A: The question asks to give restrictions must be made on x, y, and z so that the triple (x,y,z) will…

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: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

A:

Q: I need help with this assignment. they all should have 4 places after the decimal place unless the…

A: Solution:

Q: Can someone help me answer this question with all the steps thank you.

A:

Q: Let a, 1 1 -7 -7 3 and b = 3 15 h For what value(s) of h is b in the plane spanned by a, and a₂?

A:

Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

A: We have to find the equation of line in slope intercept form.

Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

A:

Q: Find the eu. f line through the Pont (-2,3,4) and Parallel to e Planes: 2x +3y +42-5, 3X+4y+52 - 6…

A:

Q: Given the set R² with the vector addition operation defined by (x₁₂1₁) (x₂, 1/₂) = (x₂+x₂₂3₁ +3₂ −2)…

A: Given a vector addition operation, we want to find the zero vector for the set .

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: Engg. Maths Memory Based Q. If the vectors (1. | 1. 2), (7,3, X. (2.3. 1) In R are Linearly…

A:

Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

A:

Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: (a) Determine all real values of b such that the set of all linear combination of u = (b, 2) and v =…

A:

Q: X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors.…

A: Obtain Kernel of T as follows.