1 Defined in P,(R), p(x)=1,q(x)=x- and h(x) =x² -: -x+- 6. Investigate whether the vectors are orthogonal. Find the orthonormal vector set, if it can be constructed.

Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

A:

Q: 2 Let L be the line in R³ that consists of all scalar multiples of the vector . Find the orthogonal…

A:

Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

A:

Q: Demonstrate that these vectors are not linearly independent. Which pairs of vectors, if any, are…

A:

Q: 2 line of the following vector field that passes through the specified point z²k; (2, 1, 3)

A:

Q: Use the inner product (u, v) = 2u;V, + uzV2 in R2 and the Gram-Schmidt orthonormalization process to…

A: In the question it is given basis for ℝ2 is -2,1,2,1 and also given inner product by…

Q: The dimension of the vector space ii2×3 is equal to 6. Select one: True O False

A:

Q: 2/159 The commercial airliner of Prob. 2/90 is redrawn here with three-dimensional information…

A: Given :The commercial airline of Prob. 2/90Magnitude=90 kN.We fine y-and z-coordinates of the point.…

Q: The vectors --[+]»-[i]»-[3]m² -]»-[3]»=[] V2 = span R2 but do not form a basis. Find two different…

A:

Q: What are the conditions for a set of vectors {ai , i ∈ [1, N]} to form a basis for an N dimensional…

A:

Q: 2. Show that the following set of vectors are orthogonal, then normalize the vectors to make an…

A:

Q: The set of vectors u, = , and u2= are having rank 3 Linearly dependent Linearly independent having…

A:

Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: If F1 and F2 are two forces simultaneously acting on anobject, the vector sum F1 + F2 is called…

A: We know, The vector sum of all of the forces acting on a body is a single force called the net force…

Q: Project the first vector orthogonally into the line spanned by the second vector. 2 3 -2

A:

Q: 2. If a --i+3j-k and E-2itj-3K decompose vectoes E into the sum of two vectors, one is paralled and…

A: This question can be solved using the concept of condition of two vectors to be parallel and…

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: Determine

A: Length of all vectors is 1.

Q: 8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and…

A: Just assume a vector and apply criteria of perpendicular of two vectors ..as I have done solution in…

Q: Linear Algebra

A: According to the given information, it is required to construct an orthonormal basis of the set:

Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

A:

Q: 7. For the vector ū = (1,2,3), compute the 1-norm, the 2-norm, and the 0-norm.

A:

Q: (a) show that the set of vectors in Rn is orthogonal, and(b) normalize the set to produce an…

A: a) given , 3,3,3,-2,0,2    So ,   3,3,3 -2,0,2  ⇒6 +0-6=0 Hence , vectors are orthogonal .

Q: What will happen if the Gram–Schmidt process is applied to a set of vectors {v1, v2, v3}, where v1…

A:

Q: (9) Find a vector parameterizat1on of the line r(t) which passes through the points P = (2, –6, 4)…

A: The given points are P=(2,-6,4) and Q=(3,5,-3). We have to do vector parametrization. We subtract…

Q: Suppose we have n> 1 vectors in R" vector space where the ith element of the ith vector (for 1 ≤ i…

A:

Q: Find the stable vector of P || -

A:

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

A:

Q: The set of vectors u1 = , and u2 = are %3D having rank 3 Linearly independent having rank 1…

A: Given- The set of vectors u1=<1,-1,3,-1> and u2=<1,-1,4,2> To Check- If they are…

Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Show that there are infinitely many vectors in R^3 with Euclidean inner product with (1,-2,4)is zero

A: Given vector is (1,-2,4) in R^3

Q: 6.) Find a vector equivalent to the vector PQ with its initial point at the origin. = (;-2), Q =…

A:

Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: (a) show that the set of vectors in Rn is orthogonal, and(b) normalize the set to produce an…

A:

Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

A:

Q: Determine which set of vectors form an orthonormal. a) b) c) d) None of these 11L

A:

Q: 2. If a set of vectors contains at least 2 vectors that are scalar multiples of each other, then the…

A:

Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

A:

Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

A:

Q: 1. Compute the angle Pair Of vectors in Standard inner producy on Mzz. between tre following Mzz…

A:

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

A:

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: 6. Compute the projections of [1, – 1,0, 1] on the vector [0, 1,0, 2]. |

A: Let v = [1, -1, 0, 1] and u = [0, 1, 0, 2]

Q: 2. Find a 3 x 4 matrix R for which the null space of R is spanned by the vectors -- -E 0. v = u =…

A:

Q: Calculate the first two vectors generated by the Gauss-Seidel method.

A: Gauss Seidle method

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.