9. V =|-1 Write the vector as the linear combination of the basis vectors 3 4 and u, =|- 3 u, = 2 ,uz = 6. Uz %3D 3

Q: Q2: For the vector x=[1,5,7,9,13,20,6,7,8] replace the first five elements of vector x with its…

A: For the vector x = [1,5,7,9,13,20,6,7,8] the maximum of all co-ordinates is, 20 & the minimum of…

Q: 46 4 and j -3 Express the vector v as a linear combination of a -12 y. ||

A:

Q: 6. Consider the vectors u = (1,–2), v = (4,3), and w = (9,4). Find scalars k and k2 such that w =…

A:

Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: Let u=(-1,37 and u =< 2,-57 Find the Component form of the vector Su-V

A:

Q: (a) What is the sum V of the twelve vectors that go from the center of a clock to the hours 1: 00,…

A:

Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

A:

Q: 18 as a linear combination of a and y Express the vector v y.

A:

Q: Find the stable vector of 1 3 4 4 P = 4 %3D 3 7

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Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

A:

Q: 2 1 3. Show that that the vector u = |-5| is a linear combination of the vectors v1 = |-3 3 2 2 V2 :…

A: The given vectors are: u=2-53, v1=1-32, v2=2-4-1  and  v3=1-57 Vector u=2-53 is a linear combination…

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: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

A:

Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

A:

Q: 2. Express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of…

A: position vectors

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: 5. Express the vector having magnitude 7, and direction 13 degrees (when drawn in standard…

A:

Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

A:

Q: 5. Express the vector having magnitude 7, and direction 13 degrees (when drawn in standard…

A: Solve the following

Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

A:

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: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

A:

Q: linear algebra question:

A: The orthogonal projection is given by,

Q: 17 (c) Find a unit vector which is orthogonal to the vectors -1 2 and 1 -3 5

A: First we will find a vector which is orthogonal to both given vectors and then we will find the unit…

Q: 11) in triple cross of vectors (A × C) × B = Cx (B × A).

A:

Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

A:

Q: (g) Can a basis for R' contain 9 vectors? Explain why or why not. 1 (h) Normalize the vector v = 1 1

A: Result: If dimension of a vector space V is n then the every basis of V contains exactly n elements.…

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

A:

Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

A:

Q: Find a vector orthogonal to (0, 1, 7) and (2i – j+ 4k) 11i + 14j - 2k 2i - j+ 11k -j + 28k 4i + 14j…

A:

Q: 50 Express the vector b = – 11 as a linear combination of the %3D – 48 - - 14 5 - 10 - | - vectors…

A: the question are based on the concept of linear combinations. we will form the system of linear…

Q: 10 Write the vector W =-10 8. as a linear combination of the basis vectors -8] 2 and u, 6. -4 u, = 2…

A:

Q: 3. 2 Find a non-zero vector in R* which is orthogonal to 1 and 2 1

A: Given vectors are 1234, 3121 and 2311. We have to find the non-zero vector in R4 which is orthogonal…

Q: 3 The vectors u = -4 and v = -12 are linearly independent. 6.

A: Given vectors : u=3-42 and v=9-126 . Therefore,  we will test these two vectors to find whether 'a'…

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

A:

Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: 2 3. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -3 and v = .3 4

A: What is the inner product of the vector space of 2 by 2 matrices. We assume it is Frobbenius inner…

Q: (1) We have the following 4 vectors v1, v2, v3 and v4. Prove that the vectors are linearly…

A:

Q: 7. Find the cross product of the vectors (a) u=(1,2,-3) v=(-4,1,2) (b) u = (0,1,- 2) v = (3,0, - 4)

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Q: 2 Find The vector novmal to The vector A=2i-3;

A:

Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

A:

Q: - Find the length of the vector -3v if v = (2, 3, -2, 1).

A: Givenv=(2,3,-2,1)-3v=(-6,-9,6,-3)

Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

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Q: Express the vector (0, -1) linear combination of the vectors (1, 1) and (-1, 1) as a The correct…

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

A:

Q: 3. Find the vector component of u along a and the vector component of u orthogonal to a for the…

A: Given that the vector u=2, 0, 1 and the vector a=1, 2, 3. We have to find the vector component of u…

Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

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Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.