Cl and ,g and e, in the definition )- 9. In order to span R? using the vectors of spanning must be G = y-2x and c, = y-x a. b. q = 2x- y and c, = y-x с. none of the above

Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

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

A: Given z=4x+yw=16x+5y-4z

Q: Let a1 and a2 be linearly independent vectors in R3, and let x be a vector in R2. (a) Describe…

A: Choose a1, a2 such that they are linearly independent in R2. Choose x ∈ R2 arbitrarily

Q: Given the vectors in 3-dimensional space is a= (a,az.az) and b= (b,b,.b,). The cross product of a…

A:

Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

A:

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: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v, and w…

A:

Q: a) If possible, express w as a linear combination of vectors u and v. w = (1,0, –7), u = (1,3,4), v…

A:

Q: If the volume of the parallelepiped determined by the vectors ä, 5, č e R³ is A cubic units, which…

A: Consider the provided question, a→∧3b→∧b→∧c→Let a→∧3b→=u→a→∧3b→∧b→∧c→=u→∧b→∧c→…

Q: Find all values of h such that the vectors {a,, az} span R?, where a1 a2

A: Given that,

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

A:

Q: Determine the value(s) of k such that the area of the parallelogram formed by the vectors a = (k +…

A:

Q: given the vectors u = (2,4) y = (- 1,3) and w = (2, -3) Determine the values ​​of α and β such that…

A: Given vectors are  U = (2,4) so we can write it as=  2i + 4j ( i is the unit vector in x direction…

Q: a. Consider the following vectors in R3 V1 = Vi = |2|,v3 1 Is the set consisting of these vectors…

A: Let's find.

Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? EN B 3 4 nob C…

A: Given:

Q: Find a vector a with representation given by the directed line segment AB. A(5, 4), B(0, 8)

A: We have to find a vector a with representation given by the directed line segment AB.

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

A:

Q: Let a, y, z be (non-zero) vectors and suppose w = 4y – 16x + 3z. If z = 4x – y, then w x+ y. Using…

A:

Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? 2 В 3 4 A C

A: topic - polygons

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

A: We have to use the equations z=4x+y and w=16x+5y-4z to describe the relationship between the vectors…

Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

A:

Q: Suppose u = (0, –2) and v = (2, 2) are two vectors that form the sides of a parallelogram. Then the…

A: This question is based on parallelogram diagonal.

Q: given the vectors from R. 203, v2 (1 3 0), v3=( 2 4 -1) 203 belongs to span{v,, V2, v3}. Select one:…

A: We have to check the span

Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: snip

A: In Euclidean geometry, the geometry in our every day experience, the…

Q: Let ABCD be a trapezoid with parallel sides AB and DC. Suppose that the length of AB is 20…

A: Two lines which never intersects each other are considered parallel lines. And the distance between…

Q: Let {v1,v2,v3} be a set of vectors in Rn. If "u" is in span {v1,v2,v3}, show that 3u is in span…

A:

Q: Define the points P(2,-2) and Q(3, 4). Carry out the following calculation. Find two vectors…

A: Solve the following

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

A:

Q: Let w, x, y, z be vectors and suppose z = -2x – y and w = 2x + 3y + z. Mark the statements below…

A:

Q: 11. Let a, =3 ,b3-5 For what value(s) of h is b in the plane spanned by a, and a2?

A: We have to find the value of h

Q: Given that the set of vectors {v1, v2, v3}, where the vectors belong to R3 are linearly independent.…

A:

Q: Let V= K? and let w be the subset of vectors in Vwhosellast coordinate is to 0. Then Shaw W is a…

A:

Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A:

Q: Let vi = 2 v2 , V3 = -3 3 Does the set of vectors {v, ,v2, v3} span R3 ? Give reason(s) for your…

A:

Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: 16. Consider this regular octagon. If AB =ü and BC =v, express each vector in terms of u and v. B C…

A: 1)from the triangle law of addition  when two vectors are moving one by another then the third…

Q: If the volume of the parallelepiped determined by the vectors d, b, čeR' is a cubic units, which of…

A: Given, 2a→∧b→∧b→∧c→ Let, 2a→∧b→=u→ Now simplifying the given equation by apply the vector dot…

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: Given vectors ū = [x, y,5] , i = [3,1, –4], and w = [7,7,7] , find x and y such that u xi = w. Тext

A: given,       u⇀=x,y,5   ,   v⇀=3,1,-4   and   w⇀=7,7,7

Q: given the vectors from R, (-5 0 3) belongs to span{v,, V2, V3}. Select one: O True O False

A:

Q: Let w, x, y, z be vectors and suppose z = -x + 3y and w = 3x – y+ 3z. Mark the statements below that…

A:

Q: Given points: A = (4, 9, 1) B = (-2, 6, 3) C = (6, 3, -2) Using norm of located vectors, prove that…

A:

Q: Given that the set of vectors {v1, v2, v3}, where the vectors belong to R3 are linearly independent.…

A: We solve this by simple definition of linearly independent set

Q: For the vector PP, , its norm satisfies PP, =2. The inscribed angles between PP, 2 2 and x-axis and…

A:

Q: For what values of a is the vector (a2, a, 1) belongs to span {x1 = (1,2, 3), x2 = (1,1,1), x3 =…

A:

Q: A- If P1(1,3, –2) and P2(4,7,-2) are two points. 1- Compute the length of 2P,P2 2- Is the vector…

A:

Q: b. Please provide a well explained answer for the follwoing. And explain how to add/subtract…

A: We have to write definition and some basic properties of vectors.

Q: Given three-dimensional vectors p, q, and r, which of the following operations is not well- o.…

A: The solution is given as