6. a. Show that the vector á of b = (3, 1, 4) and ở = (1, 2, –3). (1, 12, –29) can be written as a linear combination b. Determine whether 7 = (16, 11, –24) can be written as a linear combina- tion of p = (-2, 3, 4) and ở = (4, 1, –6). Explain the significance of your result geometrically.

Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: 3. Determine whether each vector can be written as a linear combination of the vectors in S = {(6,…

A:

Q: 2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your…

A:

Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

A:

Q: 4

A: We are given the following vectors.

Q: Write v (2,5, –4,0) as a linear combination of uz = (1,3,2, 1); U2 (2, — 2, -5,4); из %3D (2,…

A:

Q: 3. Let A be the vector (6, 7, 0, 9, 15), B be the vector (a, b, c, d, e), and C be the vector (-4,…

A: Answer:- Given, the vectors A  = (6, 7, 0, 9, 15), B = (a, b, c, d, e) and  C = (-4, -1, -2, 0, -15)…

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: Determine whether the following set of vectors are linearly independent

A: Step 1: Step 2: Step 3: Step 4:

Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express…

A: a. To express each column vector of AB as a linear combination of the column vectors of A, we can…

Q: draw the vector -u+ 2v + 4w

A:

Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

A:

Q: Let u = [1, -6, 3] and v= [-3, 3, 0]T. Find the vector w = 3u - 2v and its additive inverse. W= W=…

A: The given vectors and .We have to find the vectors and find its inverse.