18 as a linear combination of a and y Express the vector v y.

Q: 9

A: We need to determine all the values of the constant a for which the vectors

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: a) for which values on are the vectors V3 = 2 %3D 7 19 linearly independent?

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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: Q2: For the vector x=[1,5,7,9,13,20,6,7,8] replace the first five elements of vector x with its…

A: For the vector x = [1,5,7,9,13,20,6,7,8] the maximum of all co-ordinates is, 20 &amp; the minimum of…

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

Q: 46 4 and j -3 Express the vector v as a linear combination of a -12 y. ||

A:

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

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Q: Find the terminal point of a vector v = with an initial point P(0, 6, 2).

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

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Q: A vector A-xyzi+3x'yj+ (xz-y'z) k.

A:

Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩.Express y as the sum of two vectors: one parallel to x, the other…

A: Given that: x=(1,1,1) and y=(0,3, -2) are two  vectors. Let us say,  w = (a, b, c ) is a vector…

Q: Determine if the vector v is a linear combination of the remaining vectors.

A: Given vectors are: v=123; u1=110; u2=011 If the vector v is a linear combination of the remaining…

Q: a. A. vector.orthogenal.tr.Uxv.and.Txw.

A:

Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

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Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Г 13 and vz = 14 are linearly independent. Determine whether the vectors v 14

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Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

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Q: 14. Let nonzero vectors ü,ỷ,wER' be linearly independent. Show that there does not exist a nonzero…

A: We are given that three vectors in R3, u→,v→,w→ are linearly independent. We need to show, there…

Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

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Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: linear algebra question:

A: The orthogonal projection is given by,

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: 5. For which value of x do the following vectors form a linearly dependent set in R -1 y =|x, in- х,

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Q: 6. Let y = write y as the sum of two orthogonal vectors, one u = -6 in Span {u} and one orthogonal…

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

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Q: 1. Determine if the vectors e2t and e-t are linearly inde- e2t e-t pendent/dependent.

A:

Q: Which of the following vectors are linearly independent? (2) (0) 21

A:

Q: 1. Show that the given vector functions are linearly independent (-00,00). on x; (t) =

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

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Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

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Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Determine the vectors axe linear yy independent -3 2. 8. O ON

A: For linearly dependent determinant  of matrix is zero D=0

Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

A:

Q: 5. For which value of x do the following vectors form a linearly dependent set in R x,

A:

Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

A:

Q: 13. Describe the vector that translates LMN to L'M'N’. 6. L' L 2 N' M -6 -4 -2 4 6 N2 M -4 -6 4,

A: Translation vector

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = &lt;0, 1, 2&gt;  and  w = &lt;1, 0, 1&gt; Let av + bw = 0 =&gt; a(0, 1, 2) + b(1, 0,…

Q: Determine all values of the constant k for which the vectors and are linearly dependent.

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Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

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Q: 11) in triple cross of vectors (A x C) x B = C x (B x A).

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Q: Can vector w = 3 be written as a linear combination of v₁ = 4 4 vector w belong to span{v₁,v₂}? V₂…

A: