Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered basis for M₂x2. Find the coordinate

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: ✓3.10 Project the vectors into M along N. {(*) Ix+y=0}, (b) (¹). (c) M={ M={ '(^).. () () N = {…

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Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in…

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Q: IP IE Express the vector + =[] y as a linear combination of = [2] -[1] and y=

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Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

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

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Q: Find the stable vector of 1 3 4 4 P = 4 %3D 3 7

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Q: Let x 4 || - N and y = Find the vector v = 3x - 4y and its additive inverse. 18 [2] 4

A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

Q: Find the coordinate vector [x] of x relative to the given basis B= (b₁,b₂}. 1: 2 MAM-HA = -5 b₁ -3…

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Q: (a) [1 2]. [–1 1] (c) [1 3], [2 – 3]. [0 2] (d) [2 4], [-1 2] (b) [0 0]. [1 1]. [–2 – 2]

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Q: 16. Let F = 2a, - 6a, = 10a- and G = a, + G,a, + 5a;. If F and G have the same unit vector, G, is…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

A: We have to show that-w is not a linear combination of u,u and v are linearly independent,w is a…

Q: I need help with this assignment. they all should have 4 places after the decimal place unless the…

A: Solution:

Q: Find the stable vector of 7 P = 2/7 M5 iii

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

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Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: Suppose |||| = 5 and |||| = 6, and assume and y are orthogonal. Then ||-||²7

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Q: 3.2.1 Vector Cross Product Let vectors: A = (1, 0, −3), B = (–2, 5, 1), and C = (3, 1, 1). Part…

A: Since, you have posted a question with sub-parts greater than three. We will provide the solution…

Q: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

Q: Verify that (AB)T = BTAT.

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Q: Find the length of the projection of [−8 −7]onto the vector [−7 5]   Its written vertically…

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Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: .3.21. Determine whether the given vectors are linearly independent or linearly dependent: 2 (¹).…

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Q: Q10. 4 A is a condtant vector and R= 3xí + 3yj +3zk, then grad ( 3A.-R) = ? (a)A (6)3A (C) JA /d)…

A: Let us have the constant vector A=ai^+bj^+ck^ Here, a,b,c are fixed real numbers. Now,…

Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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Q: 5. [6.1] If vector ā reaches from the origin to point (5, –7), determine the magnitude of ā.

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Q: 2.30 Let r denote a position vector r = x= xê, (r² vector. Use index notation to show that: (a) ²…

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

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Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

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Q: 3.10. Rotate the vectors by 30%. *:[],三闾

A: We have to Rotate the given vectors by 30°.

Q: Let = [-5 1] and = [6-6]. Find the following vectors. [ = -6y = [ w = 5x – 6y = [ | v=5z ]]

A: A detailed solution is given below.

Q: Compute the quadratic form x Ax for A= Xx₁ 12 - a. x = b. x= 1 X2 a. x¹Ax= 3 2 [1] 10 C. X = and…

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