9. (a) Show that the three vectors v = (0, 3, 1, – 1), V2 = (6, 0, 5, 1), and v3 = (4, –7, 1, 3) form a linearly dependent set in Rª. (b) Express each vector in part (a) as a linear combination of the other two.

Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

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Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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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: 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: 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: Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V4 = (…

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Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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

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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: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

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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: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…

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Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

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

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Q: Are the vectors (-3,0,4), (5,-1,2), and (1,1,3) linearly independent in R3?

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

A: Given the three vectors

Q: (a) Show that the vectors v1 = (1, 2, 3, 4). v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

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Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

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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: Consider the vectors in R2 3 2 (3) Express as a linear combination of the vectors Select one:…

A: Here we have to find the linear combination.

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: ) Show that the three vectors vị = (1, 2, 3, 4), v2= (0, 1, 0, – 1), and v3 = (1, 3, 3, 3) form a…

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Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

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Q: The set of vectors u = , and u2= are Linearly dependent having rank 1 having rank 3 Linearly…

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Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: Show that the column vectors (1,1,2,4),(2,-1,-5.2) (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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

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Q: 1. Consider the vectors [2, 1,0, 2), [3, 1, 0, 1), [1, 1,0, -1) in R. Decide whether they…

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Q: Which of the following sets of vectors are linearly independent?

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Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

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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: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

Q: The set of vectors u1 = , and u2 = are %3D having rank 3 Linearly independent having rank 1…

A: Given- The set of vectors u1=<1,-1,3,-1> and u2=<1,-1,4,2> To Check- If they are…

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: ) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

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Q: 4). Determine whether the set of vectors in P, is linearly independent or are linearly dependent {2…

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Q: 6.) Find a vector equivalent to the vector PQ with its initial point at the origin. = (;-2), Q =…

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Q: 1. determine whether each vector linear combination of the vectors in S. S= {(1, 2, -2), (2, -1, 1)}…

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Q: b) Express the vector (–1,5, –6) in R³as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

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Q: Show that the column vectors (1,1,2,4), (2,-1.-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are…

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Q: 2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 =…

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Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: The vector 1 is in Span{ V2, ., Vm } if and only if ( V1..., Vm ) are linearly dependent. O True…

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Q: Prove that two vectors are linearly dependent (taken as a set of vectors) if and only if one vector…

A: Let X and Y be two vectors. Suppose these two vectors are linearly dependent. [To prove: One vector…

Q: 6. Determine if the vectors vi = (1,–1,3, –1), v2 = (1, –1,4, 2), v3 = (1, –1,5, 7) are linearly…

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