of the old set. 8.) Suppose that u, v, and w are three different vectors in R and suppose that w is in span(u, v). Can we then conclude that u is in span(v, w)? Explain your answer. Proof Skills in 2.3 O ix is

Q: 10. Given two vectors u = [6,2] and v=[-2,1], determine the projection of u on v.

A: #10

Q: Let v = −→P Q, where P = (−2, 5), Q = (1, −2). Which of the following vectors with the given tails…

A: Given :                             v = PQ→where P (-2,5) and Q (1,-2)So,       v = [1-(-2)]i +…

Q: Let u, V and w be three vectors in R. Which of the following is not defined for all u, v and w?…

A: Given u , v and w be three vectors in R3 . To find which of the following is not defined :-

Q: Assume that the vectors a, b, c, and d are defined as follows: a = (2, 1) b = (6, 3) c= (4, -7) d =…

A: Given, b=⟨6,3⟩c=⟨4,-7⟩

Q: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

A:

Q: For what values of b are the given vectors o , (smallest value)

A: Let m→=-12, b,3 and n→=b, b2,b  If m→ and n→ are orthogonal.

Q: Determine whether given vectors spans in 3 R ? S = {(2, -1,4) , (3, -3,5) ,( 1,1,3 ) }

A: Given- S=2,1,4,3,-3,5,1,1,3 To Determine- Whether the given vectors span in R3 or not. Concept Used-…

Q: Let a and b be vectors in R3 with Ja| 3 and = 4. If the angle between a and b is |b| (2а + b) . (а —…

A: Given |a| = 3  and  |b| = 4 And the angle between a and b is pi/3

Q: Use the accompanying figure to write each vector listed in Exer- cises 7 and 8 as a linear…

A: Given - Use the accompanying figure to write each vector listed in Exercise 8 as a linear…

Q: n Let ú and ú be two nonzero vectors in R" for which ú + 2v is orthogonal to ủ – 20. What is the…

A: We have to find the ratio

Q: The measure of the angle between the three- dimensional vectors u = (0, -1, -3) and v = (2,3,-1) is…

A:

Q: Let v and w be vectors in R° such that v · w = Which of the following is a possible angle between v…

A:

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

A: Spanning set : Let us consider a vector space V and S be a subset of V then the set S is said to be…

Q: 9. Let b, and b, be any real numbers with | b, |31 and | by151. Let u- VI - bịi + b, Vĩ – bị j +…

A: Consider the given vector: Here the objective is to prove that the given vector is a unit vector.

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

A:

Q: Suppose that u, v, and w are vectors such that «u, V> = 6, «v, W> = - 7, cu, w> = 13, ||u||= 1,…

A:

Q: Which of the following sets of vectors are bases for R2? (а) (2, 1), (6, 0) (b) (5, 3), (—10, —9)…

A:

Q: et u, v, w be vectors. Which of the followings are meaningful? (Hint: The notation x means cross…

A: solution

Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

A:

Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

A:

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: let V be the Euclidean space R3 with the standard inner product.

A: Given:          u = 11-2  and  v = a-12 To find :             The values of a, for which u and v…

Q: Answer the following muitiple-choice awestion belo algubra H17. S is a collechun of S vectors mR".…

A: Span of s Mcqs

Q: Prove the property if a and b are vectors and m is a real number.a . b = b . a

A: Proof : let a and b are vectors and m is real number. To prove :   a . b= b . a

Q: Given the vectors vi = (1,1, –1), v2 = (1,2,3) and v3 = (0,1,1). S = { v1, v2, v3} set R3 does it…

A: 3 vectors span R³ if they are linearly Independent. Vectors are linearly Independent if their…

Q: Determine whether given vectors spans in R? S={(2,-1,4).(3,–3,5).(1.1.3)}

A:

Q: The value of k is 5 so that the vectors u= (30, 6) and v = (5, -k) are orthogonal. O True O False

A:

Q: In R, you are given the vectors -10 u = 4 and v = -7 -39 If w = -9 belongs to Span(u, v), then what…

A: Consider the provided question, vectors,u=-34-4  and  v=-10-7-4and if w=-39-9z  belongs to Span…

Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: Assume that the vectors a, b, c, and d are defined as follows: a = (8, 7) b = (6, 3) c = (2, -1) d =…

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: Compute (m +n)´ if m and n are two unit vectors and the angle between them 30°.

A:

Q: Consider the following vectors. u = (5, 0), V v = (1, 1) Find the lengths of u, v, and u + v. ||u||…

A:

Q: State if the following statement is true or false. The set of vectors B= {v=(4,2,3),u%3D(-2,0,-7),w…

A:

Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

A:

Q: Which of the following vectors is coplanar to [1, 1, 1] and [1, 2, 3]? O a) [4, 2, -2] b) [5, 7, 6]…

A: Given vectors  [1,1,1] and [1,2,3] For coplanar with another vector, the determinant should be zero.…

Q: Which of the following sets of vectors spans R^2?  A. {(1, 1), (–2, –2)} B. {(1, 1), (1, 2)} C.…

A:

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: Which of the following sets of vectors are bases for R? (a) (2, 1), (3, 0) (b) (4, 1), (-7, -8) (c)…

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: Let u, v and w be vectors. Which of the followings are meaningless? (Hint: The notation . means dot…

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: Let ữ, v, w e R* be three nonzero vectors and { u', V} be a linearly independent set. Then which of…

A:

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

A:

Q: 4) Which of the following vectors is parallel to the line L: x = 1 -t, y = 2 + 3t, z = 5 + 2t? a)…

A: According to the guidelines we are answering first question. Please repost the remaining.…

Q: Pls help ASAP

A:

Q: 6. Given the vectors u1 = | 2, u2 = |3,u3 | 4,u4 = consider the following two statements. Decide…

A:

Q: 3. Suppose u and v are two vectors in R and u # v. Which of the following options are possible for…

A: When two vectors are multiplied    1) yes  2) no

Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: Let u, v and w be three vectors in R³. Which of the following is not defined for all u, v and w?…

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.