Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R. Explain, using linear algebra, why it is (generally) impossible to find a vectro (x, y, z) that is orthogonal to u, v, and w. Your explanation should refer to the properties of a relevant system of linear equations.

Q: In Exercises 9 and 10, write a vector equation that is equivalent to the given system of equations.

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Q: b) Give an example of 5 linearly independent vectors in R*, or explain why it is impossible to do…

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Q: (b) Find a homogeneous linear system of two equations in four unknowns whose solution space consists…

A: We will assume an arbitrary point on the R4 space and find the equations needed by applying the…

Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Let a1 and a2 be linearly independent vectors in R3, and let x be a vector in R2. (a) Describe…

A: Choose a1, a2 such that they are linearly independent in R2. Choose x ∈ R2 arbitrarily

Q: Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

A: Here we use property of orthogonal vectors and show that is U, V, W is a basis there is no X=(x,y,z)…

Q: [C] Is the system of vectors X1 = (2, 2, 1)", dependent? Ху — (1,3, 1)7, X3 = (1, 2, 2)" linearly

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Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: A sum of scalar multiples of two or more vectors (such as c,u + c,v + c,w, where c, are scalars) is…

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Q: Determine whether the set of vectors in M2,2 is linearly independent or linearly dependent.

A: Let they are linearly dependent Then there will be scalars x and y so that

Q: Prove that the set of vectors B = {(1,2,3), (3,2,1),(0,0,1)} is linearly independent and spans R³.

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Q: Without doing any calculations, explain why the following sets of vectors are linearly dependent:…

A: Since you have posted multiple question with multi part we are supposed to give solution of first…

Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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Q: Determine if the given vectors are coplanar u = 2i - j - k; v = 4i + 3j + 2k; w = 6i + 7j + 5k

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Q: Consider the vectors in R 1 1 1 V2 =| 2 V3 = | 4 -1 1 Write the system, which corresponds to the…

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Q: t, v1 = (1, 2, −1), v2 = (2, −1, 3), v3 = (3, 2, 3). Determine whether the vectors v1, v2, v3 are…

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Q: Give an example of three linearly dependent vectors in R3 such that none of the three is a multiple…

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Q: Show that if {V1, V2} is a linearly independent set of vectors and v3 does not lie in Span {V1, V2},…

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Q: 2. Rearrange the equations to form a strictly diagonally dominant system. Apply two steps of the…

A: The complete solutions are given below

Q: If a, B, y are linearly independent vectors of V(R), show that a + B, B + y, Y +a are also linearly…

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Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: (b) Determine whether the vectors, , and are linearly independent or linearly dependent.

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Q: (b) Find a homogeneous linear system of two equations in four unknowns whose solution space consists…

A:

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: Suppose vi, V2, V3, b, d are vectors in R". Further suppose that -vi + v2 + vz = -b, 2v1- 2v2 + v3 =…

A: Given v1,v2,v3,b,d are vectors in Rn.-v1+v2+v3=-b ,…

Q: B)Find value of h for which the vectors are linearly independent, justify answer

A: 2-24 , 4-67 ,-22h

Q: Determine whether the vectors v, = 1 10 and 11 are linearly %3D V3 independent.

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Q: This Linear Algebra and Multivariate Calculus Course ,      Consider the vectors u = [3,-1,2], v…

A: given the vectors u = [3,-1,2], v = [-2,0,2] and w = [1,-1,-2 ]. we need to find the angle between…

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=<-1,0,1> v=<3,2,1> w=<0,1,2>

Q: Which of the following sets of vectors in R' are linearly independent? (a) (-3,0,4), (5,-1,2),…

A: Linearly independent set: The set of vectors x1, x2, ..., xn in a vector space V is said to be…

Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: Let a1 , a2, a3 be linearly dependent vectors in R3, not all zero, and let A = [a1 a2 a3]. What are…

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Q: Find the vector form for the geveral selution to the system of equations. X, - X, + Zxg - xy - Xx=-8…

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Q: Exercise 6 Is the set of vectors V = {i² + 2t – 1,3t + 5, -t² + t + 6} linearly dependent?

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: Find all real values of c such that the vectors [2 and +3 are linearly independent.

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Q: (bj Prove that if in a system of non-zero vectors they are pairwise orthogonal, the system is…

A: Given: Consider the system of non zero vectors and they are pairwise orthogonal,  and show that…

Q: Given that the set of vectors {v1, v2, v3}, where the vectors belong to R3 are linearly independent.…

A: We solve this by simple definition of linearly independent set

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: Find all values of h such that the vectors {a,, a2, a3} span R, where 4 a2 a3 еВook Submit Answer 0.…

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Q: Consider three vectors ) --() 1 1 2 V1 V2 V3 W 3 1 3 2 1 | (a) (b) Are v1, V2, V3 linearly…

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Q: 3. Give an example of vectors in R3 that are linearly independent. (show works)

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Q: Consider the vectors from R 1 1 v, = 2 V2 a V3= 4 %3D 5 a) Create the system which correspond to the…

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Q: Determine if the vectors of R³; vị = (1, –3,0), v2 = (3,0,4) and vz = (11,–6,12) are linearly…

A: Given vectors are: v=(1,-3,0) v=(3,0,4) v=(11,-6,12) Form a matrix by having rows as given vectors.…

Q: Let u, v, w be three linearly independent vectors in a vector space. Determine a value of k, k . so…

A: Given that: u, v, w are three linearly independent vectors in vector space and S={u-5v,v-8w,w-ku}

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.