4.6. Is (4, –1,7) a linear combination of (1,2, 1) and (2, 1, 3)? 4.7. Find two different combinations of u = (1,3), v = (2, 7) and w = (1, 5) that produce b = (0, 1). Question: if I take three vectors u, v and w in the plane, will there always be two different combinations that produce b = (0, 1)?

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

A:

Q: Which of the following sets of vectors in R are linearly dependent? Note. Mark all your choices. O…

A: Let us consider a set of vectors v1,v2,......,vn then the set is linearly independent if…

Q: 3. Let V = P (R) (or P(R) if 2 = 0). How many vectors does a system of linear inmependent vectors in…

A:

Q: (6) Is the following set of four vectors in R4 linearly dependent? S = {(1, 2, 3, 1), (-1, 0, 2, 1),…

A:

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A: We want to find linearly dependent vectors. We know that a set of vectors is said to be linearly…

Q: 8. Given u = (1, 3, 2) and v = (3, 2, 4), find a) u + 2v b) ||u-v|| c) vector w if u + 2w = v

A:

Q: If k is a real number, then the vectors (1, k), (k, 5k + 14) are linearly independent precisely when…

A:

Q: Suppose u = (-6,4, –5). Mark each vector below with a "T" if it is perpendicular to u, and an "F" if…

A: The given vectors u=-6, 4,-51. 2, 3, 02. 5,-2, 23. 9,-24,-304. -5,-4,-1

Q: Let u= (1,1,−2) and v= (a,−1,2). For what values of a are u and v orthogonal?

A: Two vectors are said to be orthogonal to each other if their dot product is zero. we are given u=…

Q: Which of the following sets of vectors in R are linearly dependent? Note. Mark all your choices. O…

A:

Q: Which of the following sets of vectors in R° are linearly dependent? Note. Mark all your choices. O…

A:

Q: 1. Show that the set as; S = {(1,1,1), (2,3,3), (0,1, 2)} spans R3, write the vector (4, 6, 7) as a…

A:

Q: Which of the following sets of vectors in R are linearly dependent? Note. Mark all your choices. O…

A: The detailed solution is given below  Thank you

Q: 1.2.5 If a, b, and c are linearly independent vectors in R", prove that a+b, b+c, and a + c are also…

A:

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A: Set of vectors x1, x2, ...xk is independent vectors if for scalar a1, a2,..., an.…

Q: If k is a real number, then the vectors (1, k), (k, k + 56) are linearly independent precisely when…

A: If k is a real number, then the vectors (1, k), (k, k +56) are linearly independent precisely when k…

Q: 3 Let λ ER, and consider the vectors u, v, w E R³ defined by u = (3, 3, −6) v = (6, 7, -12) w = (3,…

A:

Q: Which of the following sets of vectors in Rª are linearly dependent? (a) (3,8, 7, – 3). (1, 5, 3, –…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: Show that the set as; S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R^3, write the vector (4,6,7) as a…

A:

Q: 1. Given the following set of vectors in P2: S = {u, v, w} where u = 2 + x², v = 3 – x and w = 5 –…

A:

Q: 5. Suppose vectors ū and i are linearly independent. Show that the vectors w = 2u+3ū and 7= ū+ū are…

A: if u and v are linearly independent then for au+bv=0 implies a=0 and b=0

Q: 5. For which value of x do the following vectors form a linear dependent set in R3? (글글씨 x, ; V2 =…

A:

Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

A:

Q: Given the following set of the vectors from M22 1 1 10 0 3 4 6 21 0 2 2 1 8 6 4 6 We can not express…

A:

Q: If there are no vectors in the set S = {a1; a2; a3} from R^3 who is a multiple of one of the other…

A:

Q: If u = x²+2x-y and v = - 2xy - 2y, then the vorticity vector is - 3yk 10 -yk 1O IIO yk IIO

A: Given u=x2+2x-yand v=-2xy-2y

Q: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

A:

Q: For what value or values of the constant u are the following vectors are linearly related and are…

A:

Q: Which of the following sets of vectors in R3 are linearly dependent? Note. Mark all your choices. O…

A: Notice that 12, -42, 18=62, -7, 3. So,  is linearly dependent. We observe that  is linearly…

Q: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

A: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

Q: Which of the following sets of vectors in R' are linearly independent? (a) (-3,0,4), (5,-1,2),…

A: Linearly independent set: The set of vectors x1, x2, ..., xn in a vector space V is said to be…

Q: 3 The vectors u = -4 and v = -12 are linearly independent. 6.

A: Given vectors : u=3-42 and v=9-126 . Therefore,  we will test these two vectors to find whether 'a'…

Q: Which of the following sets of vectors in R° are linearly dependent? Note. Mark all your choices. O…

A:

Q: Consider the vectors u =(1,0,4) and v =(-4,11,-4) in R3. If it is known that -3u" +w =v° then w…

A: From the given problem: u=1,0,4; v=-4,11,-4 So, -3u=-31,0,4=-3·1,-3·0,-3·4=-3,0,-12

Q: 12. Given the sct of vectors S = {(6,2,1), (4,-3, 1), (5, 8, 2)} of R, is this set linearly…

A: Given: S=6, 2, 1, 4, -3, 1, 5, 8, 2 To check: Whether the set S is linearly independent and the…

Q: 5. For which value of x do the following vectors form a linearly dependent set in R x,

A:

Q: 11. For what values of c are the vectors [-10 -1, 12 1 2], and (1 1 cl in Ra linearly dependent? 12.…

A:

Q: 2.10 If A, B, and C are noncoplanar vectors (that is, A, B, and C are linearly independent),…

A: It is given that,  A, B and C are linearly independent vectors. We have to determine that whether…

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices. O…

A: The objective of the question is choose the correct option that is choose the linearly dependent…

Q: For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and…

A: The vectors are linearly independent if the matrix formed from these vectors has non zero…

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices. O…

A: Two vectors are linearly dependent if they are collinear. Here for the set of vectors a→=(0, -8, 9),…

Q: (1) Suppose that {r, y, z} is a linearly independent subset of vectors in R". Show that {x - z + y,…

A: Result:  A set of vectors v1, v2, …, vn is said to be linearly independent, if a1v1+a2v2+…+anvn=0…

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices. O…

A:

Q: 4. Find the components of the vector with the opposite direction to that of the vector from M(2,3,5)…

A: First we need to find the vector and then find the opposite components of it.

Q: 6. Let ū, ū, and w be vectors. Explain why any linear combination of ū and ở is also a linear…

A: Consider any two vectors x→ and y→, let the linear combination of these vectors be denoted by a→,…

Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

A:

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: then C(A) contains all vectors by by ()- If b2 such bs that O a. b 2b, and b, 3b, O b.by b ba Oc 2b…

A:

Q: 4. For which value of k the vector u = -2 is a linear combination of the vectors 3 3 V1 = 0 and vz =…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.