y = -3 7 4 6] 0 Z = 1 -8 15 -7

Q: Consider the vectors (2, 1, 0, 2], [3, 1,0, 1], [1, 1, 0,-1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: refer  to  image  below.

A: Lineraly dependentv3={-1/3} v1 +{1/3} v2Explanation:Step 1: Step 2: Step 3: Step 4:

Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

Q: Represent the vector with respect to each of the two bases { ] y = B = B2 =

A:

Q: Let A = 3 2 1 -14 -5 -2 12 -4 -3 a) Beside the origin, does A fix any other vector? -5 b) Find the…

A:

Q: 1) a) Find all vectors such that X = b) Explain why there is no such that X =

A: It is required to find all the vectors v→ such that 1,2,1×v→=3,1,-5. It is required to explain why…

Q: Let m (1, 2, 3) and n (5, 3,-2). Find the vector projection of m onto n, that is, find proj- m. You…

A:

Q: If a,b,c are vectors such that a.b=a.c,a×a=a×c, then show that b=c

A: Given, a,b,c are vectors such that a·b=a·c, a×a=a×c To prove: b=c

Q: Determine which pairs of vectors in Exercises 15–18 are orthogonal. 8 -2 a= [&] - [ ³ ] b = -5 -3…

A: The given vector is, a=8-5,b=-2-3. The pair of vectors are orthogonal if the dot product of the…

Q: Determine if the following vectors span R³. 2 ~-~-8 U₁ = -2, U₂ =

A: Given that u1=2-20, u2=1-11

Q: 5) Write the analytical expression of the unit vector for F= 400 i + 700j - 400 k %3D

A:

Q: The projection of the vector 21+3ị – 2k on the vector i-2j+3k is 2 14 V14 1 V14 O None of the…

A:

Q: 3 Find the length of the vector i -1 -5

A: For any vector x= [a  b  c] it's length is given by ||x||= √(a^2+b^2+c^2) Given vector x=[3  -1  -5]…

Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: Consider the points A (10, 9) and B (0, – 7). Find the vector AB. АВ

A:

Q: What does the span of the following vectors define geometrically? 2 4 23 7

A: To determine: The span of the following vectors geometrically. 123, 247

Q: Write down the 2 by 2 matrix that a) project every vector onto x¡ axis. b) rotate a vector clockwise…

A: We have to solve given problem:

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: In the given diagram, which is the equivalent of vector

A: sum of vectors of closed triangle is 0 if we choose one direction -- Here if choose anticlockwise…

Q: Let A: = -7 2 6 -4 -1 - 9 6 5 7 5-8 3 Find a nonzero vector v in Col(A).

A:

Q: Determine which pairs of vectors in Exercises 15–18 are orthogonal.

A: Two vectors u and v are orthogonal if            u.v = 0

Q: 4.) Are vectors Linearly independent? 2 3

A:

Q: 1. Find A-C|(B – D) using the following vectors: A= C= D=

A:

Q: That is not correct. The first Vector answer is [-2/3, -1/3, -2/3] (column wise format.)

A:

Q: Chapter 11, Section 11.3, Question 025a Find the vector component of v = 2i – j+ 3k along b = 4i +…

A: given vector v=2i-j+3k  and b =4i+8j+8k

Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: {a} = C1 %3D {a, b} = C2 {a, b, c} = C3 %3D {a, b, c, d} = C4 where 4 a = b =| 2 c = -1 d =| ? ?…

A:

Q: In exercises 11–16, find two unit vectors orthogonal given vectors. 11. a = (1,0, 4), b = (1, –4, 2)…

A: