a +c a) Let S = {[a – b] |a, b E R}. Find three vectors in R° so that each vector in s b-a can be written as a linear combination of the three vectors. Are these vectors linearly independent? Justify your answer. 1 2 -2 1 -1 01. Determine whether the rows of A are linearly 1 b) Let A = [! 2 4 -5 4 -2 -4 4 -1 independent. Evaluate | – 2A2| and |3A-11.

Q: Determine if b is a linear combination of the other vectors. If so, express b as a linear…

A: topic - vectors

Q: a) Given the vectors in M22 . 1 1 2 3 31 22 1 2 21 Show that they are linearly independent. b) Find…

A:

Q: a+c] a) Let S = a -b b R. Find three vectors in R3 so that each vector %3D [b-al in S can be written…

A: As this is multiple number of questions. According to our company guide lines, we should answer only…

Q: Find

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Q: E a + c] a) Let S Find three vectors in R3 so that each vector in S can be written as a linear…

A: This question is related to linear algebra.

Q: Find all values of h such that the vectors  {a1, a2}  span  R2,  where a1 =   −5   h,    a2 =…

A:

Q: Given x=(1,-2,-1,a) and y=(3,3,-2,1) are two 1x4 row vectors, where "a" is some constant, which of…

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Q: 15. Given three independent vectors w, "'z innd wz, let 2 2=[Wi #2 #3 2 1 0 1 c Then, the vectors v,…

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Q: Assuming a,b, y1,y2,y3 are all dimensional vectors, order matric A= (a,y1,y2,y3), B=(…

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Q: Determine if v is in the set spanned by the columns of B. 3 -3 2 - 6 9 -7 8 -8 B = 6 - 2 10 V = 8 6.…

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Q: 2 x=| 2 as the linear combination of the vectors u 1 Write your answer in the form x=av+bv+cw for…

A: Topic:- vector algebra

Q: Express the indicated vector w as a linear combination of the given vectors v, and v, if this is…

A: We use the definition of the linear combination of vectors to write the vector w as a linear…

Q: Determine if v is in the set spanned by the columns of B. 2 -3 2 - 4 6 -7 9 - 4 B = v= 6 -5 15 4 6…

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Q: a) Find the value(s) of c for which the following vectors v, = ,V2 : and v4 are linearly…

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Q: We have three vectors ủ, v and w in R4: 1 2 1 -1 1 (7a) Are these vectors ū, v and ú linearly…

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Q: For what value or values of k the vectors V1 = (1,0, –2,0), V2 = (-1,k,–2,0), V3 = (1,1,1,2) are ▼4…

A: A set of vectors are linearly dependent if there exist scalars not all zero such that  . A system…

Q: 4. Given vectors: ū=(4, 9), v = (-8, 15) and w=(2, 10) b) Write ū as a linear combination of and w.

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Q: -2 Is the vector x = 6 a linear combination of vi = 1 and v2 2? 8 3 O No, because av1 + bv2 = x has…

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Q: Find a set of vectors {ū, v} in Rª that spans the solution set of the equa W - = x = y + 4z 0, 5w+…

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Q: 4. Let Ā = -(1+ 2 )î + 7j – 5k , B = xî + (6 +0)j – 2k and Č = (8 + 2 )î – 2k, find the following:…

A: A = -(1+2)i + 7j -5k = -3i + 7j -5k B = xi +(6+0)j-2k = xi + 6j -2k C =(8+2)i  -2k = 10i -2k

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

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Q: HW/ O Find A.B, ĀXB For As i+ 3j+2k , B = K O let À - i+2j-K , B=-i+j+ K , E=i+k> Dz i+2j=K_ which…

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Q: 1 4 Let v, V1 v2 V3 - 4 V2 V3 - 5 p= - 2 and A = %3D 4 60 56 a. How many vectors are in {v,, V2,…

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Q: For what values of h are the vectors -7 3 and 2 OA. The vectors are linearly dependent for all h.…

A: The given vectors are -732 and -146h

Q: Which of the following pairs of vectors are linearly independent? u= (1,2) and w = (2,1). Ou= (1,0)…

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Q: Given vectors v1 = 1 2 1 v2 = −2 1 2 and v3 = −1 3 3 in R3 , determine if w = 5 5 1 can be written…

A: Linear combination of vectors

Q: 41. For what values of t are the following pairs of vectors parallel? (a) 27 + (r² + 71 + 1)j +ik,…

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Q: 19. For two non – zero vectors ā' and b,if ||a' + || = ||a'||, then which of the following is…

A: Given : For two non-zero vectors a→ and b→,  ||a→+b→||=||a→|| Use the property ||a→||2=a→.a→

Q: 5. Suppose vectors ū and i are linearly independent. Show that the vectors w = 2u+3ū and 7= ū+ū are…

A: if u and v are linearly independent then for au+bv=0 implies a=0 and b=0

Q: Given the vectors ü = -i - 2j + 3k and i = - 2i + 6j – 3k. _17. The unit vector in he direction of v…

A: A unit vector perpendicular to a vector a→ is represented as follows: a^=a→a→

Q: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

A: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

Q: O let A = i+ 2j-K , B=-i+j+K,' Ezi+K>,5z i+2j=K مواری which vectors are: @ perpendicular parallel O…

A: A¯.B¯=(1*(-1))+(2*1)+(1*(-1))=0 Thus A¯ and B¯ are perpendicular to each other.…

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

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Q: Assuming a,b, y1,y2,y3 are all dimensional vectors, order matric A= (a,y1,y2,y3), B=(…

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Q: Assuming a,b, y1,y2,y3 are all dimensional vectors, order matric A= (a,y1,y2,y3), B=(…

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Q: 5: The vectors v = [1 2 9] and w= [2 4 18] are linearly independent vectors. O True O False

A: We will find the given two vectors are linearly independent is true or false in the following step.

Q: Given the vectors 1 1 0 0 2 3 1 2 3 in R3. Given vectors are linearly independent. Select one: O…

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Q: Find a set of vectors {u, v} in R¹ that spans the solution set of the equations 3z Sw-x-y 3w + 2xy…

A: Spanning set

Q: Determine if b is a linear combination of the other vectors. If so, express b as a linear…

A: we can b as a linear combination or not

Q: (b) If u and v are vectors in R' such that ||ū|| = 1 and |||| = 2 then u · i# 10.

A: The angle between two vectors and Dot product in R3 is related by

Q: 5. a. Explain why the vectors ả = (-2, 3) and b (3, –1) span R². %3| b. Determine the values of p…

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Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b…

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Q: 5. Let A =-ai+3j–2k and B = 4i + ßj+8k (a) Find a and ß if A and B are parallel. (b) Determine the…

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Q: 4. Let Ā = -(1+ 2 )î + 7j – 5k , B = xiî + (6 +0)j – 2k and ĉ = (8 + 2 )î – 2k , find the following:…

A: As per company guidelines we are supposed to answer only one question at a time. for solution of…

Q: If A= (3/2) i –(½) j + k and B= i+j+2k, what is the value of A x B? Are the vectors orthogonal? O…

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Q: Given x=(1,-2,-1,a) and y=(3,3,-2,1) are two 1x4 row vectors, where "a" is some constant, which of…

A: We are asked to find which statement is false.

Q: Find a set of basic vectors {ü, i} in R“ so that every vector in the solution set of the equations…

A:

Q: Determine if b is a linear combination of the other vectors. If so, express b as a linear…

A:

Q: 4. For which value of k the vector u = is a linear combination of the vectors k .-E)--- ------ 3 2 3…

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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.