8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

Q: The vector z = (2 + 2i) ( -V3 + i) lies in * the

A: The vector equation is z=2+2i-13+i.

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

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Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: (b) How can you use vectors to determine whether four points in 3-space lie in the same plane? 2.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: Construct the vector 0.8 b+1.4 a having initial point P.

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Q: 7. "Let &, n, ở be real numbers and consider vectors (1,5,8²); (1,n,n²); (1,0,0²). Determine the…

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Q: The vectors --[+]»-[i]»-[3]m² -]»-[3]»=[] V2 = span R2 but do not form a basis. Find two different…

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Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: Write down the general solution of Ax = b in parametric vector form.

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Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: 4

A: We are given the following vectors.

Q: The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector…

A: If vectors are parallel then cross product will be zero check they parallel or not

Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

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Q: Find a basisfor the span of the given vectors.

A: Consider the provided matrix. 1-11,120,011,212 Find a basis for the span of the given vectors.

Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

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Q: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

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Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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Q: linear algebra question:

A: The orthogonal projection is given by,

Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

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Q: Find the coordinate vector of Prelative to the basis S= {P1P2P3} P1 = 1+x +x², p2 = x +x, p3 = x:p =…

A: Given: p=6-x-9x2p1=1+x+x2p2=x+x2p3=x2

Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

A: Note:  part(b) is the independent subpart of part(a) and also it is incomplete. so part (b) can't be…

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

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Q: 7. For the vector ū = (1,2,3), compute the 1-norm, the 2-norm, and the 0-norm.

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Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: 18 as a linear combination of = 8 Express the vector i and j =

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Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

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Q: 50 Express the vector b = – 11 as a linear combination of the %3D – 48 - - 14 5 - 10 - | - vectors…

A: the question are based on the concept of linear combinations. we will form the system of linear…

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 all values of the scalar kfor which the two vectors are orthogonal.

A: Two vectors u and v are said to be orthogonal if u·v=0. Given that, u=1-12 and v=k2k-3 We have to…

Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

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Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: Express the vector x as a linear combination of the u's. U₁ = 0, U₂ = 5, -1.4 U3 Ox=-3u₁ +4u2 +243…

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Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

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Q: Express the vector x as a linear combination of u,, u2, and uz. – 2 3 - 2 ,x = 0 u2 = 5 u3 = – 4 u1…

A: Given u1=-201, u2=356, u3=-26-4 and x=-99-38

Q: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

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Q: Find the stable vector of P = 2 2 2 3 -|3

A: Let stable vector is w= [x  y  z ] So, So, equations to solve

Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

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Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Find a vector b such that compab = 2. If a = ⟨3,0,−1⟩

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Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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