11 6 linear combinations of x, y, and z, or show that it cannot be done. Let x = 120 and z = TTTT If v 240 and w= 9 either write v and w as

Q: If A × B ={(p, q),(p, r), (m, q), (m, r)},     find A and B.

A: A will be the set of the first ordinates  And B is the set of the second ordinates

Q: 4. If u = (-3, 2), v = (-4, –6), find 4u – 7v %3D

A:

Q: Let S be a linear transformation from R³ to R2 with associated matrix Let T be a linear…

A:

Q: 9. Let u = : (4, -1), v = (0, 5), and w = (-3, -3). Find the com- ponents of a. u + w c. 2(u - 5w)…

A: We have u=(4,-1)v=(0,5)w=(-3,-3)

Q: 3 Let x = (9, −9, −4) and y = (-6, 6, -9) be in R³ and a be in R. Then ax + y = ( ,23).

A:

Q: If a = (1, 2, 1) and b cross products. 1. a × b : = 2. b xa = = (12, 15, 1), find the following

A:

Q: 9. Express the gcd(117,213) as a linear combination of s and t such that gcd(117,213) = 117s + 213t…

A: To write the gcd(117, 213) as a linear combination.

Q: 10. Find a and ẞ such that c = αa + ẞb, where a = (-3,0,2), b = (0,-1,2), and c = (-6,5,-10).

A:

Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

A:

Q: Consider the subset of P3 Q = {−6x² + 4x − 6, −24x² + sx + 6, 2sx + s} Find the two values of s for…

A: In this question, we will find the values of 's' for which a given set is linearly dependent.

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: verify that (AB)T = BTAT

A: Given matrices: Now,

Q: Compute u – 3v, u v and u x w.

A:

Q: Let u = , v = and w = . Now, i = is a linear combination of ü, v and w. That is, i = aju + azv +…

A: ANSWER:

Q: Show how v is orthogonal to any linear combination formed by w1 and w2

A:

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^