Write y as the sum of a vector in Spanfu} and a vector orthogonal to u and u Let y = That is, Find vectors x and w such that x E Spanfu, w l u, and y xw

Q: The component of the vector (-5, 0, –3) onto the vector (3, –4, –2).

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Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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Q: Find the largest possible number of independent vectors among 1 Vi = V2 V3 V4 Find any independent…

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Q: Let u be the vector with initial point (2, -5) and terminal point (-1, 3).  Find the norm (or…

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Q: Find a vector of norm 1 that is orthogonal to the three vectors ü = (2,1,-4,0), v=(-1,-1,2,2),…

A: We have to find a vector of norm 1 which is orthogonal with the vectors u, v and w. Let a, b, c, d…

Q: Find two unit vectors orthogonal to both u (3, – 1, – 2) and i (0, 4, 2). Give exact values - (no…

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Q: Determine the volume of the box whose sides are the vectors (1, -2, 1), (2, 3, -2), (-1, 3, -2)

A: use determinant method to findout the volume.

Q: Find the vectors u and v whose initial point is u: (3, 2),v: (1, 4) and terminal points is (5, 6) ,…

A: Initial point is (3,2) and the ending point is (5,6) so the vector is u=(5,6)-(3,2)=(2,4)   Initial…

Q: Find linearly independent vectors which generate al lutions of Ax = 0.

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Q: Find 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

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Q: Eind vnit Vector that is ortogone a O u=(!,-!,2) and V=CO,3,1)

A: Here we have to find the unit vector orthogonal to u=1,-1,2 and v=0, 3,1

Q: Find two unit vectors orthogonal to both (2, 6, 1) and (-1, 1, 0). (smaller i-value) (larger…

A: Consider the given vectors. Cross product of two vectors is perpendicular to both the vectors. This…

Q: The cross product of the vectors u = (a,, a, az) and v = (b, bz, b,) is the vector |ijk -目 u X v =…

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Q: Find two unit vectors orthogonal to both (2, 7, 1) and (-1, 1, 0). (smaller i-value) (larger…

A: Given that the vectors are 2,7,1 and -1,1,0.It is required to find the two unit vectors orthogonal…

Q: Let(vector u)=(-2,-3), (vector v=(-3,-5) and vector w=(-2,-3). Find the vector x that satisfies…

A: u=(-2,-3)v=(-3,-5)w=(-2,-3)Calculating x:

Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

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Q: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

Q: Let ü = (– 2, 1, – 2, 1) and i = ( – 4, 5, – 1, 1). A vector perpendicular to i and v is (

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Q: In a 4-D Euclidean plane, vectoru = (a, b, c, d). In a 3-D space, vector v = (2,7,c). What is u + v?…

A: Given :  Vector u = <a, b, c, d>  Vector v = <2, 7, c>     To find the vector u + v.

Q: Calculate parallel component of vector a = [1,2.2] in the directoin of vector v = [7,7, 7].

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Q: find the diJ tance betueen the vectors

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Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x + y. :Select one…

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Q: Select all vectors perpendicular to the vector (1, 3, -5) O (2, 1, 1) O (0, 5, 3) O (1, 1, 3) O (4,…

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Q: Calculate the area of the parallelogram which is bounded by two vectors given as www ā = (x, y,z),…

A: Calculate area

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x+ y. :Select one…

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Q: A vector orthogonal to the plane through the poii (-1,0,0), (0, –2, –2), (2, 3, 4) is < -2, – 10, 9…

A: The given 3 points are A (-1,0,0) , B (0,-2,-2) &amp; C (2,3,4) Let, x1=-1, y1=0, z1=0 x2=0, y2=-2 ,…

Q: Let u be the vector with initial point 〈-2, 6〉and terminal point 〈-8, 3〉. Write u as a combination…

A: Let, x=&lt;-2,6&gt;=-2i+6jy=&lt;-8,3&gt;=-8i+3j

Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

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Q: Find a vector perpendicular to (2, −1, 10) and (1, 2, −1)

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Q: Select all vectors perpendicular to the vector (1, 3, -5). O (2, 1, 1) O (0, 5, 3) O (1,1, 3) O (4,…

A: Given query is to find the perpendicular vectors to the given vector.

Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Find the area of the parallelogram that has the given vectors u = ⟨2, −1, 0⟩,     v = ⟨−1, 2, 0⟩ as…

A: Given vectors as adjacent sides are u=2,-1,0, v=-1,2,0.

Q: Find two unit vectors orthogonal to both (5, 8, 1) and (-1, 1, 0). (smaller i-value) (larger…

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Q: Are the follovwing vectors linearly independent? ,,

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Q: Find the component form of vector v. Intital point: (1,4) Terminal point: (-3,-1)

A: The component of the vector: - A vector's components aid in the division of a given vector into…

Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

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Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

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Q: Prove that llu + vll2 + llu - vll2 = 2llull2 + 2llvll2 for all vectors u and v in Rn

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Q: find vector v that is orthogonal to vector (0,1,0,0,0) Select one: a. v=( r, 0, s, -t, w) b. v=( r,…

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Q: For the vectors u = (-2,2, -1) and v (-2,1, 3), expressu as the sum u =p n, where p is parallel to v…

A: To find the orthogonal decomposition of the vector u along and perpendicular to v

Q: Find the largest possible number of independent vectors among 、H-E~目 V1 = V2 = V3 Find any…

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Q: Find the vector in R' from point A = (-2, –3, 8) to B = (9, –4,–3). AB = help (vectors)

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Q: Let u, = (1,1,1)", u2 = (1,2,2)T and uz = (2,3,4)", find the coordinates of the vectors (2,3,2)" and…

A: Solving by linear combination method

Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: 15) If U and V are 3 dimensional vectors such that V = [ 7, -4, 10] and U = [-5, 8, 6] calculate:…

A: NOTE: Refresh your page if you can't see any equations. . find the cross product

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.