then C(A) contains all vectors by by ()- If b2 such bs that O a. b 2b, and b, 3b, O b.by b ba Oc 2b byand 3b, b d. by 2b, and by 36 23

Q: Two vectors u and v in space are if and only if u X v= 0

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: 1 If then C(A) contains all b2 3 b3 vectors b2 such that by .a O bz = 2b1 and bz = 3b; %3D %3D .b O…

A:

Q: For any two nonparallel vectors a and b, it holds that Select one: |3a + b > 3|a| + |b| 13a + b <…

A: Use vector triangle inequality

Q: u=(-2,4) and v=(4,-2) 2u= -3v= u+v= 3u-4v=

A:

Q: 4. Suppose the vectors u and w are in space R, then u - 2w and u+ 2w are perpendicular if (a) ju =…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the…

Q: If W is the set of all vectors of the a form b 2a + b Then, which of the following vectors belongs…

A: We have to find which vector belongs to W.

Q: Suppose u and v are any vectors in R³. Which of the following is not true? Ollu + vll ≤ llull +…

A: To find which of the following properties is not true.

Q: -Let 1+t and tet? be vectors in P. write the vector plt) = S+ St+2t² as the lineor combination of P,…

A:

Q: If k is a real number, then the vectors (1, k), (k, 5k + 14) are linearly independent precisely when…

A:

Q: \(\) The vectors u= and V = are not orthogonal if and only if x=-136

A:

Q: Refer to the vectors u, to ug. -5 1 1, u2 = u3 = U4 = -5 U5 4 4 Compute projs u8, where s = span{u5,…

A:

Q: 1. Show that the set as; S = {(1,1,1), (2,3,3), (0,1, 2)} spans R3, write the vector (4, 6, 7) as a…

A:

Q: For any two nonparallel vectors a and b, it holds that Select one: O O O 3a + b 3a + b 3|a| + |b|…

A: For any two nonparallel vectors a and b , it holds that

Q: (d) Let w =(-39,22), v’i=(2–5), v°2=(5,-4), v°3=(-4,-1). If possible, express w as a linear…

A: In this question we need to multiply vectors by constant and have to find values of constant

Q: Let w,x,y,z be vectors and suppose z=−4x−3yand w=−16x+4y−4z Mark the statements below that must be…

A:

Q: If a and b are two vectors in 3-space, then axb bxa. Select one: O True False

A:

Q: 3) What is the rank of the set of vectors A1 , A2 and Az given by 25 5 A2 = l12] 64 8 %3D [144]

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: Use a counterexample to show that the following statement is false: if a, b and c are nonzero…

A:

Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

A:

Q: Consider the vectors in R2 3 2 (3) Express as a linear combination of the vectors Select one:…

A: Here we have to find the linear combination.

Q: Suppose M is the set of all real column vectors in R' whose components are equal, then the basis for…

A: See the detailed solution below.

Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: If a, b, and c are three non zero vectors, such that axa= axc and a ·b = a·c, then it is true that b…

A: a→, b→ and c→ are three non zero vectors.  Given, a→·b→=a→·c→ a→·b→-a→·c→=0a→b→-c→=0Either b→=c→ or…

Q: Two vectors u and v in space are if and only if u .v=0

A:

Q: Show that the set as; S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R^3, write the vector (4,6,7) as a…

A:

Q: 9. (a) are perpendicular to each other. Determine the algebraic condition such that the vectors č=…

A:

Q: 4.5-6 Show that, for any 2-vectors a and b, and any number A between 0 and 1, ||Aa + (1 – A)b|| <…

A:

Q: For what value of k, the vectors (-1,0,1), (2,1,A) and (3k+2, 3,10) are lincarly dependent. O A. 1…

A: We have to find for what value of k, the vector -1,0,1, 2,1,4, and 3k+2,3,10 are linearly dependent.

Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: 2 Consider A = -2 null(A). 4 2 2 4 -4 -2 -2 -4 -2 0 1 Give a set of vectors that spans each of im(A)…

A:

Q: Let x,y,z  be (non-zero) vectors and suppose w=10x−5y+3z If z=y−2x mark the statements below that…

A:

Q: For any vectors u, v in R', we havelu + ū|? = [u|2 + [ū]2 True False

A:

Q: b) Let a, b and 2 be non-zero vectors such that = ax b. If s, teR and d = så + tb, then determine…

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: 3. Explain why as n goes to infinity. the entries of the vector A" 2 go to infinity, while the…

A: To solve question 3 I will take the help of eigenvalue and eigenvector of a matrix because question…

Q: 8. If the vectors in the figure satisfy |u| = |v|= 1 and u + v + w = 0, what is w ? u W V

A:

Q: Consider the following vectors á = 2ī+3j and b = -2ī+ 3k and c = −3ī + k

A: topic- projection of one vector on another

Q: (2) Given the vectors - -- -- --- 1 V1 = V2 = V3 = and w = are there scalars a, b, and c such that…

A:

Q: 1. a. If 37-2ỷ = ở and 5x - 33 = b, express the vectors and y in terms of a and b. %3D %3D

A:

Q: - ()--)- 1 Let a = 2 and b = be two vectors. What is Jal2|b|2 - |a · bl2 ?

A: Here,  Given that  two vectors  . So, we find the value of  |a|^2.|b|^ - |a.b|^2

Q: Defermine if the set of vectors is limerdy indepandat. 3. -5 3 マ -4 3.8/10

A:

Q: Two vectors u and v in space are if and only if u .v = 0

A: Condition of dot product.

Q: 17 jp 17 Jlgull>> حفظ الإجابت 3 درجات Two vectors ñ and m are said to be parallel if ñ m-0

A:

Q: 1. If vectors u (3, 3), v-(13.-7), and 2w +3u-v 2. When is it true that u+ v=v+u?

A: The symmetric property states that for all real numbers x and y, if x=y, then y = x SO,  u+v =v + u

Q: 1. Suppose that ū, ī, and w are vectors in R³ such that ūxi= (2,7, 3) and ū xũ = (-5,4,0). Find: (a)…

A:

Q: 6. Let ū, ū, and w be vectors. Explain why any linear combination of ū and ở is also a linear…

A: Consider any two vectors x→ and y→, let the linear combination of these vectors be denoted by a→,…

Q: There exist an example of 5 vectors in R4 that are linearly independent. O True O False

A: Flase Since dimension of R4 is 4 , every linearly independent subset of R4 contains at most 4…

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: • (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.