Let V = [3, – 1, – 4] and W = [0, 2, k]. Find a real number k so that V and W will be orthogonal. k =

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: If the vectors V], V2, V3, . ..,Vn € C" are of unit length and are orthogonal to each other, show…

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Q: Find the value of k such that vectors x

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Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

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Q: Let A = {a1, a2, a3} and D = {d1,d2, d3} be bases for V, and let P = [ [d¡]a [d2]A_ [dz]a ]. Which…

A: We will use the following theorem to find the correct option.  "Let B=b1, b2, b3,...,bn and C=c1,…

Q: Determine whether v and w are orthogonal given v=-5i+2j and w=2i-4j

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Q: Any vector in R perpendicular to -3 can be written in the form t, for some s, t eR

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Q: Let x = 21 +mj and ỹ = -3ī +8j. Determine the value of m if: a) x and ỹ are collinear b) x and ỹ are…

A: Answer: a) x→ = 2i→+mj→ and y→ = -3i→+8j→ are colinear if m=-316 b) x→ = 2i→+mj→ and y→ = -3i→+8j→…

Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: Her we solve the linear equation to get the solution.

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v = {8, 1) a = b =

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Q: Defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique.…

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Q: If {v, w} is independent, find conditions on the scalars k1 and k2 so that the set {k,v + w, v +…

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Q: \(\) The vectors u= and U= are not orthogonal if and only if x=-136 Select one: O True O False

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Q: Let v = (– 1, 19, 19) and w = (– 27, – 7, – 47) be ordered triples in R'. Find two scalars ci and C2…

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Q: Given K= (-2,-1), L=(2,4), M= (-3,-1) and N= (1,4), Prove that KĽ and MN are equivalent by Showing…

A: Two vectors are Equivalent if they have same magnitude and direction.

Q: Let S ={v1 , v2 , v3 } be a set of nonzero vectors in R3 such that any two vectors in S are…

A: Given:         S = {v1, v2, v3} is a set ofnonzero vectors in R3 such that any two vectors in S…

Q: Suppose v1, v2, v3 are vectors in Rn, and that u and w are both in Span{v1, v2, v3}. Prove that for…

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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: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

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Q: let v =〈−2, 5〉and w =〈3, −2〉. Find a scalar α such that ||v + αw|| = 6.

A: Given, v=-2, 5w=3, -22

Q: Determine the real number a such that u X v| and i are orthogonal, where u = 2i + 4j + 3k and v = 8i…

A: u=2i+4j+3kv=8i-10j+αk

Q: Find the value of k for which the vectors and 4 -4 are orthogonal. k =

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Q: Determine whether the set [p., pa, p3] is linearly Independent in Pa, where pi= 3+x+3x²+4x3 Pa = 4+…

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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: OABD is a square and the line segment OA, OB, OC a re represented by the vectors a, b, c…

A: In this question we will use laws of vector addition

Q: Q1. Construct an orthogonal set of vectors from the following vectors: X1 = k,X2 ,X3 %3D 14]

A: Use the usual inner product in the vectors and Gramm-smidth orthogonalisation process.

Q: Determine the real number a such that u x v and i are orthogonal, where u = 5i + j - 9k and v = 6i -…

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Q: Suppose Q : R? → R is a quadratic form such that Q(x) = 1 for all vectors X E R? Cuch that

A: Given: It is given that the quadratic function Q:R2→R such that Q(x)=1 for all vectors x∈R2 such…

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

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Q: За Let W be the set of all vectors of the form 106 6a 106 Find vectors ü and v in R such that W =…

A: W=3a-10b6a-10b9a10b W=spanu→,v→

Q: Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis,…

A: Let O is the initial point (0, 0, 0) and the vector OP, OQ and OR vector can be represented as:

Q: For each of the given vectors x, find a Householdertransformation that zeros out the last two…

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Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

Q: For which real numbers c are the following vectors linearly independent ? X1 X1 X1 %3D %3D

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Q: Let a and b be orthogonal such that |ã| = 2 and b = 3. %3D Find (b x a) x ả and |(b × å) × |

A: Given a→=2 and b→=3 We have to find b→×a→×a→   and b→×a→×a→

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 {v1, v2} be an orthogonal set of nonzero vectors, and let c1, c2 be any nonzero scalars. Show…

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Q: let A= and Describe the sed of all vectors b for which the equatiön AX=b is Consitent.

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Q: snip

A: Assume that the set 123,  41-2,  ab3 is an orthogonal. This implies that, a, b, 3·1, 2,…

Q: For each of the given vectors x, find a Householdertransformation that zeros out the last two…

A: Given Data The vector is x=-1,8,-4T   Let, x1=-1x2=8x3=-4   The expression for the Householder…

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v = (0, 12) a =

A: We can find the value of a and b as below.

Q: Suppose that ū and i are vectors satisfying ủ ở = p , ||ủ|| = q , and 3 =. Find the angle (in…

A: (a) Consider the values for p, q and r and the values for the vector u, v and dot product for u and…

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

Q: Three of the vectors of a vector space of quadratic polynomials p1 (x) = x2 – 1, p2(x) = a² + x,…

A: Solve the following problem

Q: For each of the given vectors x, find a Householdertransformation that zeros out the last two…

A: x=(3,6,2)Tx1=0 And set α=‖x‖2=7 and then set β=αα-x1=77-3=28v=x1-α,x2,x3T=(4,6,2)T

Q: Use the standard inner product on R" to determine if the vectors or functions are orthogonal. 2 -3 1…

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Q: Q1. In each part determine whether the given vectors are orthogonal with respect to the Euclidean…

A: Two vectors u , v are orthogonal if and only if u.v=0 (a) Given u = 2 , 3 , -1 , 0v = (3 , 6 , -2 ,…

Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearlyindependent. Find…