Show that v1, v2, v3 are independent but v1, v2, v3, v4 are dependent: 2 0 V2 V3= V4 3 0 0 4 Solve c1v1 + C2V2 + C3V3 + C4v4 = 0 or Ax = 0. The v's go in the columns of A.

Q: Solve the system by using the inverse, and verify by Cramer's Rule. 4) 4x1 + 2x2 = -8 2x1 + 9x2 = 12

A:

Q: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A: Given the vectors v=i−4j+2kw=3i+2j+k

Q: Find (a) u x v, (b) v x u, and (c) v x v.

A:

Q: Find u − v, 2(u + 3v), and 2v − u. u =  (6, −7, 8, 3),       v = (−2, , 7/3, −8/3 , −1)

A:

Q: Solve, z2 - 4z + 5 = 0 Given that z, = 3 + i, z2 = 4 – 3i, z3 = -1+ 2i and z4 = -2 – 5i, determine…

A: Given equation is, z2-4z+5=0 Now, z=4±16-4×52⇒z=4±-42⇒z=4±2i2=2±i So, the solutions are z=2+i, 2-i

Q: Prove V²f(r) = d²f dr² + 2 df r dr

A:

Q: If v1 =13i+79j, v2x =24, and v1 x v2 =23k , then, what is v2y and v2z?

A:

Q: 3. Solve for X Y when using row operations. 2X + 4Y = 144 X +0.25Y = 30

A: The given system of equations

Q: V(A - B) = A x (V x B) + B x (V x A) + (A - V)B + (B V)A,

A:

Q: Solve the first order PDE -2и, + 6и, — 0, и (4у, у) — 2у + 1

A:

Q: Solve z5 – V2j + 1 = 0

A: Given : z5-2j+1=0

Q: Given m = 2xe2y and n = x³e-2y. Find if J=-16x³. ax am e2y e-2y 2x2 8 3e-2y e2y 16x 8x3

A:

Q: Show that the equation (1, 2, 3) × v = (−1, 2, a) has no solutionfor a = −1

A: Consider the given: Given equation:1,2,3×v=−1,2,aLet v=x,y,z1,2,3×v=ijk123xyz…

Q: Solve the eguatoN V2x t V 3xt2 %3D

A: Given equation, 2x+3x+2=2

Q: Minimization: Z = 5X, + 6X, + 10X, + 7X, + 19X5 Subject to: %3D 5X, + X2 + 3X3 – 4X, + 3X5 2 2 -2X,…

A: In this problem we can observe that all Xj ≥0 and so, Z can be minimum 0 as all coefficients of Xj…

Q: Solve the problem. Leta₁- a₂ a3- and b- Determine whether b can be written as a linear combination…

A:

Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A: Solution:Given    v=-i+3j+2k              w=3i-2j-kFind:(a)v×w(b)w×v(c)w×w

Q: b. d.x Vx4 – 2x2 + 1 3

A: Let's find.

Q: Use Cramer's rule to solve the following system of equations: 3x1 4x2 = -5 2x, + x2 = 4

A:

Q: Let w = (2, −2, 1) and v = (4, 5, −4). Solve for u if v + 5u =3w − u.

A: Simplification of the function helps to find the vector u. Component-wise operations help to get…

Q: Find å + B, 2å + 35, |äl, and |ä – | for å = i + 2j – 3k and b = -2ï – j + 5k.

A: solution:-a→=i→+2j→-3k→b→=-2i→-j→+5k→(1)a→+b→=i→+2j→-3k→+-2i→-j→+5k→         =1-2i→+2-1j→+-3+5k→…

Q: what does P(A∩B) = if P(A)=0.63, P(B)=0.47, P(B∩A¯¯¯¯)=0.27

A:

Q: Q10): Let A 14 A 1 5 0 03 3 (a) Is 2 in the span of the columns of A? What about 2? -1 1₁ 3

A:

Q: Given u = 21+j-6k and v = i-4j+ 3k, find (u•v)v. O (u•v)v =-20i+ 80j–60k O (u•v)v=-40i–20j + 120k O…

A:

Q: 4x, +2x, + x3 = -1 -4x, — 6х, + х, +Зх, %3 3 8x, +16х, — 3x, — 4х, %3D-2 20x, +10x, + 4x, – 3x, = 4…

A:

Q: Az = b, where A = (A) 7/6 1/6 (D) [2/3] 1 3 b = 189 11 [Q] X2 Compute projcol(A) (b), the projection…

A: The matrix .The objective is to find the projection of  onto .

Q: 1 Which of the following is the reduced row echelon form of 2 -3 2 24 4 -6 -1 -1.7 -1 1 0? 0.

A:

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

A:

Q: 4. The component of 4î – 5k in the direction of 2î + ĵ – 2k is: A. 8î + j – 10k 3 3 B. 4î + 2j – 4k…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…