7. Provide a justification for your response to the following questions. a. Suppose that we have vectors in R°, Can every vector b in R° be written as a linear combination of V1, V2,• ••, whose span is R°. V10, V1, V2, ..., V10? b. Suppose that we have vectors in R°, v1, V2, ..., V10, whose span is R°. Can every vector b in R° be written uniquely as a linear combination of V1, V2,· ••, V10? С. Do the vectors ei = e2 = ez = cnan m3,

Q: Let 0 = - be the measure of the angle between the vectors u and 0.If ||T'|| = 6 and ||D'|| = 4, then…

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Q: If two vectors a+b and a-b are orthogonal, then we have la| = |b|. Select one: O True O False

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Q: Given the following vectors u'and v, find a vector w in R3 so that {u, v, w} spans R3 and a non-zero…

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: Which of the following vectors are parallel? 1. Please select the two vectors that are parallel. А.…

A: 1) Two parallel vectors a and b are of the form a=kb, where k is a constant.  We can write <12,…

Q: Find the angle between the vectors v and w in each of the following: (a) v= (4,1)T, w=(3,2)T (b)…

A: topic - angle between vectors

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 v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

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

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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: Suppose we have three distinct unit vectors a, b, andc which satisfy the following equations: (i)…

A: b × c ≠ 0b × c = bc sin θ a^nθ could be anything but θ ≠0 that means b and c are not coplanner…

Q: If v . w = 0, then the two vectors v and w are____

A: If v . w = 0, then the two vectors v and w are____

Q: For what value of t, if any, is the vector (2, -4t) paralel to the vector (4, -1) ? t O A -2 %3D 1…

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Q: In each part, find the two unit vectors in R² that satisfy the given conditions. 1. The two unit…

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Q: Given vector U= ⟨1,-1⟩ and V=⟨1,1⟩, find a linear combination of the vectors u and v of the form aU…

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Q: For what values of c are the vectors t + 3 and 2t + c2 + 2 in P1 linearly independent?

A: t+3  &  2t+c2+2 Now since these vectors must be linearly independent, therefore…

Q: Consider the following vectors: 2 3 u = 3 v = -4 W = 17 2 Express w as a linear combination au+bv.…

A: The given vectors are  u=23-1  , v = 3-42,  w= 017-7

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: If v*w=0, then the two vectors v and w are................ .

A: The question is taken from the vector in which we have to prove the given vector identity and given…

Q: 19. Which of the vectors (A)–(C) in Figure 22 is equivalent to v – w? (A) (B) (C) FIGURE 22

A: The vectors substraction: (v-w)

Q: Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find:

A: (a) The angle between the two vectors u and v is computed by the following formula. cosθ=u·v|u||v|…

Q: If the vectors V1, V2, V3, ..., Vn E C" are of unit length and are orthogonal to each other, show…

A: We will prove the given statement.

Q: Given the following vectors →u and →v, find a vector →w in ℝ3 so that {→u, →v, →w} spans ℝ3 and a…

A: Now u = {2 ,4,10} and v = {5 , -6 , 7}  We can see that u and v vectors are linearly independent.…

Q: Find cos(0) if 0 is the angle between the vectors u= 4i – 3k and v = 2i – 2j + k 2 14 15 15

A: First I have written a short note , just use them and find that  Answer is 1/3

Q: Under what conditions are the following true for vectors u and v in R2 or R3? (a) llu +vll = llull +…

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Q: One of the following vectors lies in span{ 2+x + æ2, 3+-2a2} (A) 5 + 3x + 4x2 (B) 5 + 3x + 5æ? (C) 5…

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Q: If a = 2i – j+2k and b =i+2j – 2k, find two vectors e and d satisfying all the following conditions:…

A: Let the required two vectors c and d be c=x1i+y1j+z1k and d=x2i+y2j+z2k. Now as per the given data,…

Q: For what value of t , if any, is the vector (4t, -1) parallel to the vector (4, -1) ? OAt=1 OB. t= 2…

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Q: и %3D —3і + бј, w%3 -2i – 5j u = W =

A: Here I am attaching image so that you understand each and every step. Given option are not match…

Q: In the accompanying figure, it looks as if v1 + v2 and v1 - v2 are orthogonal. Is this mere…

A: Given figure shown below.

Q: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: For what value of t , if any, is the vector ( 2t, -1) parallel to the vector (4, -1) t= 2 OA. No t…

A: Solution: The objective is to find the value of t

Q: - Let v and w be vectors such that |v| = 2, ww = 36 and the angle between v and w is T/3. Calculate…

A: This question can be solved using the concept of vectors.

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: At approximately what angle should the tails of two unit vectors a and y be placed if 2+ 7 = 1.5 60…

A: It is given that x→ and y→are two unit vectors, x→=1y→=1 Let the angle between the given two vectors…

Q: Given the following vectors: ü =, i = Find u x v.

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Q: If v = 2i – 4j and w = 4i + 2j have the same initial point, is v perpendicular to w? Why or why not?…

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Q: 3 The vectors a and b are defined by a - and Given that a + 2b = Si + 4j find the values of p, q and…

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 16i- 8j V = 3i+11j…

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

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Q: 2 Given the three vectors A = 2i +j, B = i+ k, and C = 4j, find the following (a) A. (B + C) and (A…

A: Given vectors: A=2i+j+0kB=i+0j+kC=0i+4j+0k

Q: For what values of ai are the vectors [a1,4,3] and [3,-2,12] are a) orthogonal? b) Parallel? c) Have…

A: This question is taken from the vector in which we have to find the value of a for the different…

Q: Consider the following vectors: 2 -2 and b -3 u , V 4 When b is expressed as a linear combination…

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Q: Given that the angle between the vectors a and b is n/3, then the angle between the vectors -a and b…

A: Angle between two vectors a and b is π3 Let us find the angle between -a & b  Represented in a…

Q: For each of the following pairs of vectors u and v, calculate u ∙ v and the angle ? (to the nearest…

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Q: Refer to the vectors u, to ug. 3. 4 1 , u2 u3 u4 Us = U6 = u7 ug Compute projs ug, where s =…

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Q: For what value of t , if any, is the vector (2, -4t) parallel to the vector (4, -1) No t O A. 1 %3D…

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Q: For each of the following pairs of vectors u and v, caloulate uov and the angle e (to the neares+…

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Q: 14. Given that a and bare two vectors, then the vector (a + b) × (a – b) is A. perpendicular to (a –…

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.