let u = <1, 2, 2> , v = <1, -1, -1>, w = <1, 3, -1> , and z = <2, 11, 8>. Write z = u1 + u2 + u3, where u1 is parallel to u, u2 is parallel to v, and u3 is parallel to w. What are u1, u2, u3?

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

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Q: Let u = (2, 1, –1), v = (-4, 4a + B, 2), =(a,0, 3,8). %3| Find the values of a and 8 such that: u is…

A: Given: u=2,1,-1, v=-4,4α+β,2, w=α,0,3β; u∥v and v⊥w

Q: Calculate the component of v = 〈− 2, 1/2 , 3〉along w =〈1, 2, 2〉.

A: Given: Vector, v=-2,12,3 Vector, w=1,2,2

Q: 14) Determine whether u and v are orthogonal, parallel, or neither for u = and V = .

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

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Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (−1,…

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Q: Let u=(1,2,3) and v=(4,5,6). Then u and v are A. Pointing in the same direction B.Pointing in…

A: Let u=(1,2,3) and v=(4,5,6) When two vectors are in same direction then the angle between the…

Q: Suppose that u, v, and w are vectors such that «u, V> = 6, (v, w> = - 7, ku, w> = 13, lu||= 1,…

A: The axioms of vector operations are as follows: &lt;u+v, v+w&gt;= &lt;u,v+w&gt;+&lt;v,v+w&gt; &lt;u,…

Q: Let w, x, y, z be vectors and suppose z = 4x + y and w = 16x + 5y – 4z. | Mark the statements below…

A: Spanning set : Let us consider a vector space V and S be a subset of V then the set S is said to be…

Q: Let u=(-1,2,-7) and v=(4,-8,28). Then v and u are A. Pointing in the same direction B.Pointing in…

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Q: Show that if u and v are orthogonal, then || u * v || = || u || || v ||

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Q: (d) Let u, v, w be arbitrary vectors in R³. What does the set of all combinations, Cu + c2v + C3w,…

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Q: Which vector is collinear with [2, -3]? [2, -6] O [-4, 6] O(-2, -3] O [12, 18]

A: We have to find the vector

Q: determine whether the given points are coplanar. A(0, 0, 4), B(6, 2, 0), C(2, -1, 1), D(-3, -4, 3)

A: Consider the given points as follows.…

Q: Which of the followings are false? I. L, : x = 1 +t, y= -2+ 3t, z = 4 – t and L2 : x = 2s, y = 3+ 8,…

A: We need to check whether lines interests or not

Q: find u ·v. u= [ 1,√2,√3, o],v= [ 4, -√2,0,-5]

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Q: Determine whether u and v are orthogonal, parallel, or niether. u=(-4/3,5/2) v=(16,-30)

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Q: determine whether the given points are coplanar. A(0, 1, 2), B(-1, 1, 0), C(2, 0, -1), D(1, -1, 1)

A: Given, A(0, 1, 2), B(-1, 1, 0), C(2, 0, -1), D(1, -1, 1)

Q: Use vectors to decide whether the triangle with vertices P(3, -1, -4), Q(4, 2, -6), and R(8, 0, -7)…

A: Given : Vertices of a triangle P(3, -1, -4), Q(4, 2, -6), R(8, 0, -7)   To find : The given…

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: Let u = (a, b, c) and v = (9, 10, 11). If u is parallel to (1,0, –1) and the proj along v is 10 202…

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

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Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−1, 8⟩

A: Given that v = au + bw. Substitute u =&lt;1, 2&gt; and w= &lt;1, -1&gt; in v.…

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

A:

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (1,…

A: Given u=1,2 and w=1,-1 , v=1,-4we write v is a linear combination of u and w if possible .

Q: Let u (a, b, c) and v = (9, 10, 11). If u is parallel to (1, 0, –1) and the projection of u along v…

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

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Q: Determine whether u and v are orthogonal, parallel, or neither.u = (1, −1), v = (0, −1)

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Q: What is the direction of u= (2,–3,–6).

A: Direction of a given Vector.

Q: Plot the points in same three-dimensional coordinate system and determine whether u and v are…

A: The graph is shown below:

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (0,…

A: Here u = (1, 2), w = (1, -1) and v = (0, 3) Since v is a linear combination of u and w So consider v…

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: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨4, 5⟩

A: we have to find a and b such that v=au+bw where u=1,2 and w=1,-1 and v=4,5. the given vectors are:…

Q: Find the distance between u and v and determine whether u and v are orthogonal, parallel, or neither…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Suppose that u, v, and w are vectors such that Evaluate the given expression. u-v-2w, 4u+vi= (u, v)…

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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: Given u⃗ =⟨2,−5⟩ and v⃗ =⟨4,−4⟩, find the dot product u⃗

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Q: Let ữ, v, w e R* be three nonzero vectors and { u', V} be a linearly independent set. Then which of…

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Q: Find (u, v) for (u, v) = 2u,v, +3u, v, +u,v, defined in R, where u (9,0,-3) and v (8, 2,17). A. (u,…

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

A: u = (0, 3, −4), v = (1, −8, −6) We need to determine whether u and v are orthogonal, parallel, or…

Q: Let u, v, w1, w2, and w3 be vectors in Rn. If u and v can both be written as linear combinations of…

A: According to the given information, Let u,v,w1,w2,w3 be vectors in Rn and u and v can be written as…

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

A: It is given that,  v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−6, 0⟩

Q: Let u = (a, b, c) and v = (4, 5, 6). If u is parallel to (1,0, –1) and the projetuutuTu aiuny v is 8…

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Q: Determine whether u and v are orthogonal, parallel, or neither u = ⟨2, −3, 1⟩, v = ⟨−1, −1, −1⟩

A: Given: u=&lt;2,-3,1&gt;, v=&lt;-1,-1,-1&gt; To determine: Determine whether u and v are orthogonal,…

Q: Let u = (a, b, c) and v = (7,8, 9). If u is parallel to (1,0, –1) and the projection of u along v is…

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Q: If vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1), what are the values of a, b, and c ?

A: Given : Vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1). That is

Q: Let u = (1,0, –1) and the projection of u along v is (a, b, c) and v = (2, 3, 4). If u is parallel…

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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: Please Help

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Q: Determine whether u and v are orthogonal, parallel, or neither u = ⟨7, −2, 3⟩, v = ⟨−1, 4, 5⟩

A: Given: u=⟨7,−2, 3⟩, v=⟨−1, 4, 5⟩

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.