et §, ŋ, o be real numbers and consider ctors (1,5,§³); (1,ŋ,n³); (1,0,0²). Determine e conditions &, ŋ, ơ to ensure that the 3 ctors are linearly independent.

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: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

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Q: orthogonal

A: We have   u=111    and v=2-12 are two column matrices  . We have to find the value of  k so that…

Q: Suppose , t2, ., , are linearly independent. Prove that S is linearly independent where (a) S=…

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Q: Verify the orthogonality p

A: answer is in next step

Q: 26. Let u = (2,3,1), v = (1,3,0), and w = (2,23,3). Since (1\2)u- (2\3)v - (1\6)w = (0,0,0), can we…

A: It is given that u=2,3,1, v=1,3,0 and w=2,23,3. Also, 12u-23v-16w=0,0,0. To prove or disprove that…

Q: Show that u and v are parallel if and only if u×v = 0.

A: The cross product of two vectors are defined as u×v=uvsinθ. Two vectors are parallel if the angle…

Q: Let u (a, b, c) and v = (4, 5, 6). If u is parallel to (1,0, –1) and the projection of u along v is…

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Q: Let L, be the line passing through the points Q-(-1, -3, 1) and Q-(3, 3,-1). Find a value of k so…

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Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal…

A: Given that a is orthogonal to b So a·b=0also we have c·b=2

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: Suppose that a linear transförmation / satisfies T(u,) = T(u,) = -1 -2 Find T(4u, - 3u,). T(4u, -…

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Q: Find a vector a with representation given by the directed line segment AB, where A(-4, 0, 1) and…

A: A=-401,  B=18-1 the vector a is given by  a=B-A

Q: 4-Find the coordinates the front trace F for line AB, if A(2, 1, -2) and B(3, 3, -5). * O (1,-1) O…

A: A=(2,1,-2) B=(3,3,-5)

Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: Find the cross product a × b. a = (4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a…

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Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, = (6, 0, 5, 1); v3 = (4, -7, 1, 3) form a linearly…

A: Given vectors are: v1=(0,3,1,-1), v2=(6,0,5,1), v3=(4,-7,1,3)

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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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: 1. Let a = (1, 1, –1) and b = (2,4, 6). Find the cross product a x b and verify that it orthogonal…

A: Given: a=1, 1, -1b=2, 4, 6 To Find:  To find the cross product a×b, and, to verify that it is…

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

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Q: Find a vector å with representation given by the directed line segment AB, for A(-1, 1) and B(3, 2).…

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Q: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

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Q: Let u = (1,2,3) and v = (2a,2a,a2) Which of the following values of a ensures that u and v are…

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Q: "Span(u1,..., in) = Span(71,..., Tn, w) if and only if J1,..., Un, w are linearly depen- dent."

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Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

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

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Q: Suppose the vector ū =<3,1,-47 is translated so that it's heach is at the point C-1,2,3). where ito…

A: Given that the vector u→ = 3,1,-4 is translated such that its head is at the point (-1,2,3). We have…

Q: Find all values of c so that (2, 1, c) and (c – 1, 2, 2c) orthogonal. are

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Q: Determine k so that the vectors (1,–1, k - 1), (2, k,-4) and (0, 2 +k,-8) in R linearly independent.…

A: The detailed answer and explanation is given below:-

Q: Let u = (2, 1, – 1) - (-4, α + β 2) w- (α, 0, β ) Find the values of a and ß such that u is parallel…

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Q: Write v as a linear combination of u,, u2, and uz, if possible. (If not possible, enter IMPOSSIBLE.)…

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Q: Check the set 4 2 3 Mas(R) = 11 is linearly dependent or linearly independent

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Q: Find scalars a, b, csuch that au + bv + cw = = (-6,12,4) u = (-1,0,2), v = (2,2,–2), w = (1,–2,1)

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Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

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Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: If an unknown vector X satisfies the relations X·b = β and X×b = c, express X in termsof β, b, and…

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Q: Find w such that 2u + v u 3w = 0. (0, 2, 7, 5), v = (-8, 4, -3, 1) 1 -- (-) W = 3 -

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Q: Suppose that ú, v and w are any three vectors in some R". Show that the set of three vectors: S =…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Let L, be the line passing through the points Q-(1, -4, 5) and Q-(-1,-7, 2) and let L2 be the line…

A: To find: The intersection point of the lines L1 and L2. Given information: The line L1 passing…

Q: Determine every c Є R, for which the vectors [c,1,c], [5,c,4], [9,1,c] are linearly dependent.

A: We will use the property of vectors to determine the values of c for which the given vectors are…

Q: O let )ارارا ره( - V Vz = (i) show linearly independent if that )اراواو 2 - V is set generated by…

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Q: Determine whether u and v are orthogonal, parallel, or neither.

A: Given vectors are u=2,18 and v=32,-16 Given vectors can be written as: u=2i+18j and v=32i-16j We…

Q: Let L, be the line passing through the points Q, (5,-2, –3) and Q,-(-4, –11, 6). Find a value of k…

A: Equation of line in 3D