Which of the following vectors are linearly independent? B) [1 2 3] 37 206 S75 R이 기이 46l GaF

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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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: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

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: Suppose that u and v are vectors in R' both of length 2/2 and that the length of u – v is also2 /2.…

A: The solution is give as

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: 8 Find a vector of length: (2) (+) 3 a 10 units which is perpendicular to (a -4 b 3/2 units which is…

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Q: Are the following vectors linearly independent? Yes No , ,,

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Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: Suppose that uj and u2 are orthogonal vectors, with u1 = 2 and u2|| = 4. Find |5u1 - u2 ||. ||5u1 -…

A: We have to solve given problem: Let  U1=(a1,a2)  U2=(b1,b2)5U1-U2=5(a1,a2)-(b1,b2)…

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: Two linearly independent vectors in R3 span R2, is that true

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Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

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Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

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Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Are the Following Vectors Linearly Dependent or Independent? 1) (3,4), (4,3) Ans. Indep

A: We have to check the vectors are linearly independent or dependent (3, 4) , (4, 3)

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

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Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

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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: 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: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors <-14x, 2,1> , <2, 3x2, 10> To find:- positive value of x when both…

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: what is the terminal point of a vector with initial point that Ar (-1,0is equivalent to u 3,4 O B3)…

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Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

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: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

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Q: 3. Find two unit vectors that are orthogonal to both j +2k and į -2j + 3k.

A: Solution is here

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: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: In what direction should one move from the point (2, 3) to increase 4x?y most rapidly? Present your…

A: The solution is given below

Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: 2. For what values of h the vectors , ü2 = 9 ,ūz linearly independent? are

A: To find : For what value of h  given vectors are linearly independent    We have given the…

Q: Find the vector of length 10 with the same direction as w = (2, V2, V3).

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: 2 3. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -3 and v = .3 4

A: What is the inner product of the vector space of 2 by 2 matrices. We assume it is Frobbenius inner…

Q: What value(s) of a are necessary for vectors i = (2, a), and w = (4a, 3) to span R?

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Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

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Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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Q: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

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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…

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