2. Given a trapeze ABCD. It is known that AD and BC are parallel and AD:BC= 3:2. Find the base decomposition of the vector BD in the basis a BA and b=CD.

Q: The set B= {2+z, 6+3z + 3z,- (23+9z + 12z*)} is a basis for P Find the coordinates of p(z) = - (73 +…

A: Coordinates

Q: 2.Show that the following Vectors form a Wasis for Ps. 4.ct-11,(t-1,(t-1)?

A: Given that the vectors are 1,t-1,t-12,t-13.It is required to show that the following vectors form a…

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

Q: Given the ordered basis B = {ui U2 = 13 with respect to B. -12 find [v]B, the coordinates of v = Ex:…

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Q: For what value(s) of k are the vectors u = in R orthogonal? k v= -2

A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

Q: What is [v]B, the coordinates of v = with respect to the standard basis B : of R?? Ex: 5 : [v]B =

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Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out c) e1 × e3

A: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T to Find e1 × e3

Q: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in…

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Q: For which value of a , the vectors î +} – k , î – 2î + 3k and 3î + a ĵ+ 5k are coplanar? -3 O 3 O 4

A: The given three vectors are                                              A→=i^+j^-k^…

Q: Which of the following vectors form an orthogonal basis? BBA 2 1] [0 a) -4 b) -2 2 Lo 1] 3 Lo. 2 2…

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Q: Consider the following three vectors a, b and c 10 -4|,b 5,c = 7 a = 3 Lt + 3. For which values of…

A: To find the value of t.

Q: Question 7. Show that if =0 and u - = 0, then i = 0. Let i, u be two linearly independent vectors in…

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Q: Given that A=2i+j-k, B=4i+2j+ck, find the scalar c such that: 1- A & B are orthogonal 2- A & B are…

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Q: 3. Find the following unit vectors: a. aCD in RCS b. aDE in CCS C. aEC in SCS

A: aCD in RCS is to be calculated: Converting D from CCS to RCS xD=5cos π=-5yD=5 sin π=0zD=-12 Hence,…

Q: 27. Given the vectors a and b, where a = 21 – 2j + 2k and b = 3i – j + 2k are coplanar vectors, a x…

A: Given vectors are a=2i-2j+2k and b=3i-j+2k are coplanar vectors. To find: a×b Solution: We have…

Q: Use the polygon law of addition to draw the resultant vector ( å + b) + ở for the following yectors.

A: The given vectors are added

Q: Given the ordered basis B , U2 5 find (v]B, the coordinates of v : with respect to B. Ex: 5 (v]s

A: Given: and Notice that v=u1. So, it can be observed that v=u1+0u2.

Q: If A = 6i + 7j – 10k, B = – 4i + 5j + 6k, C = 10, and C is perpendicular to both A and B, %3D write…

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Q: 4. Given the two vectors rA =-ax - 3ay - 4az and re= 2ax + 2ay + 2 az and point C (1, 2, 3) find: a)…

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Q: Find the vector projection of OA = (4, 3) on OB = (4, −1).

A: This is a basic vector problem

Q: The vectors A = 2i + 5k and B = 4i + 3j + k has: a) Ā || B b) A1 B c) 0 = 61.743°

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Q: Given the following vectors, let W Span{v, v2, vs}. v3 (a) ( . Is z in W? Why or why not? (b) ( Find…

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Q: Given v = - 7i + 5j and w= -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

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Q: Match each of the following vectors with its magnitude. t=(-7, 1) a. 5√2 u = -21-8j b. 2√√5 a vector…

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

A: Note:- We are entitled to solve only the first question, unless specified. Given vectors: a=3i-j+4k,…

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

A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

Q: Let Pa represents multiplication by 1+t? with respect to the basis B = {1,t,ť²} for P2 and BU{t,t*}…

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Q: -() --() --() 14. Let ei = e2 = ez = 1 3 Show that {e1, e2, e3} is a basis of R3 and write v = (66,…

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Q: 3. Find the length of the following vector : ā = 4i +2j – 4k .

A: Given vector a = 4i + 2j - 4k We  have to find the length of the vector

Q: The set B = {3x² – 4, 152² – (20 + 2x), 38 + 4x – 27x²} is a basis for P. Find the coordinates of…

A: Given, the set B=3x2-4,15x2-20+2x,38+4x-27x2 is a basis for P2. We have to find the coordinates…

Q: . Prove that (only one): E - 4y-V3ay is a unit vector? a- F 2 b- A = 6ax - 3a, + 2a, and B = 3a, +…

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Q: 2. Given the two vector combinations a + 4b = 4i + 4j + 6k, a - 2b = i+7j +3k, find a and b.

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Q: 2. Given the two vector combinations a+ 4b = 4i + 4j + 6k, a- 2b =i+7j + 3k, find a and b.

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Q: Given the vectors V1 = (x, 1,1), V2 = (1, x, 1) and V3 = (1,1, x). S = { V1, V2, V3} of the set Find…

A: 3 vectors form a basis of R3, if they are linearly Independent. Vectors are linearly Independent if…

Q: ,B = the standard basis, C - {[; -}-[; :)-8)-[: 9]} in 22 (a) Find the coordinate vectors [A] and…

A: The standard basis B for M22 is {e1,e2,e3,e4}.

Q: Let a = (5, 4) and b = (1, –5). Show that there are scalars s and t so that sa + tb = (-13,-22) You…

A: Given, Let a=5,4,b=1,-5 And sa+tb=-13,-22

Q: Given two vector fields E = 5xya, + 6(x + 3)a, + 8z'a, D = yza, + xza, + xya, (a) Evaluate C= D+E at…

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Q: 3. Which of the following statements is correct concerning the vectors in the diagram? (а) а-Ь-с (b)…

A: Note that the magnitude and direction of a vector does not change if it is translated from one place…

Q: nd the length of the basis of the parallelogram having the following measurement area 343 CM square…

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Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

A: (a) To show that triangle ABC is a right angled triangle, use scalar product of vector, that is…

Q: Let a = (4, 5) and b = (2, –2). Show that there are scalars s and t so that sa + tb = (2, – 20) You…

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Q: Given the ordered basis 5 6 ,A2 8 B A1 7 7 4 Аз ,A4 -5 8 5 20 find AB, the coordinates of A = 1 with…

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Q: In P, consider the basis B- {6,6} where 1 %23 b2 I – 4 Task Find the coordinates of vector w = 2z +…

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Q: 11 If m = 2i + 3j + 5k & ñ = i + 2j + 2k find the projections of m parallel and perpendicular to n.…

A: If m→=2i+3j+5k & n→=i+2j+2k, then to find the projections of m→ parallel and perpendicular to…

Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

Q: Let TilPe > Pz , T (ax?+bx+c) = 2Qx+ b. Then the basis of NIT) is

A: Just use a definition of Nullity of transformation.

Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

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Q: thogonal basis for W:

A: Orthogonal decomposition of vector