5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every vector belong to R3 can be written as a linear combination by x1, x2 and x3. %D %3D %3D O True O False

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: 5. Show that if each of the vectors {Bo, B1,...,B,} is a linear combination of {a1,a2,...,a,}, then…

A:

Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

A:

Q: Show every vector a in R² can be written as a linear combination of and

A:

Q: Two vectors in R- are linearly dependent if and only if they lie on a line through (0,0). Select…

A: It is false.

Q: (6) Is the following set of four vectors in R4 linearly dependent? S = {(1, 2, 3, 1), (-1, 0, 2, 1),…

A:

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: A set of 5 vectors in R6 cannot be linearly independent. True False

A:

Q: 8. Suppose v1 is a vector of all entries 1 in R"¹ space, which we call "1-vector". What is ||v1||2…

A: Given that, Suppose v1 is a vector of all entries 1 in ℝn space, which we call 1-vector. What is…

Q: 1.2.4 Prove that vectors (1, 1, 1)", (2, 1,0)", (3, 1, 4)", and (1, 2, –2)" are linearly dependent.…

A: Let v1, v2, v3 and v4 are given vectors that is v1=111  ,  v2=210 , v3=314 and v4=12-2 Claim:    v1…

Q: -91 Let y = -9 and u = -6 *₁ = -4. Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

A:

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {1 + 3x…

A:

Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

A:

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b,…

A:

Q: 4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal…

A:

Q: 7 Prove or give a counterexample: If v1, V2, . . . , Vm is a linearly indepen- dent list of vectors…

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: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

A:

Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

A:

Q: 1.2.5 If a, b, and c are linearly independent vectors in R", prove that a+b, b+c, and a + c are also…

A:

Q: solve using the concept of rank.

A: Given set of vectors is: S = {[4     1     2], [2      5      -5], [2      -1        3]} We have to…

Q: ) Let 1 3 2 -2 1 -2 2 8 6. be given vectors in R³. Determine if b is a linear combination of v1, v2…

A:

Q: 14. Let nonzero vectors ü,ỷ,wER' be linearly independent. Show that there does not exist a nonzero…

A: We are given that three vectors in R3, u→,v→,w→ are linearly independent. We need to show, there…

Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

A:

Q: linear algebra question:

A: The orthogonal projection is given by,

Q: 5. For which value of x do the following vectors form a linearly dependent set in R -1 y =|x, in- х,

A:

Q: 7. Provide a justification for your response to the following statements or questions. b. True or…

A: We need to give the justification for the given, that weather each statements (b),(c) and (d) are…

Q: 8. Determine whether the set of vectors in Pz is learly independent or linearly dependent. S= {…

A:

Q: Let v1, v2, vz be the vectors in R defined by 30 -17 7 -3 v2 15 V3 = -14 -12 -14 18

A: Solution is given below:

Q: how that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A:

Q: linear algebra

A: To prove the linear independence of the three given vectors.

Q: If there are no vectors in the set S = {a1; a2; a3} from R^3 who is a multiple of one of the other…

A:

Q: If there is v1 = (1,3,3), v2 = (0,1,4), v3 = (5,6,3) and v4 = (7,2, -1) is the set of linear…

A:

Q: 1. Consider the vectors [2, 1,0, 2), [3, 1, 0, 1), [1, 1,0, -1) in R. Decide whether they…

A:

Q: 3- Suppose that A = {x1 = (2,1,3), x2 = (2,0,1), x3 = (3,0,4)} then [A] = R³, then the scalars we…

A: We will use the fact that any arbitrary vector in  R3 is of the form (x,y,z).

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: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

A:

Q: Let u = [4 -6 -4] and v = [3 -6 0]. Find the vector w = 6ủ – 20 and its additive inverse. [ -w = |

A:

Q: 1. a) Let x is n-vector and p and q are two constant n-vector. is f(x) linear, or affine or neither?…

A: As per our company guidelines, we can solve first question for you. If you want other questions to…

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

A:

Q: 1. determine whether each vector linear combination of the vectors in S. S= {(1, 2, -2), (2, -1, 1)}…

A:

Q: 7) Determine whether the sets of vectors are linearly independent. а) {(-1, 2, 4)), (5, -10, -20);…

A: According to Bartleby guidelines I am supposed to do only first two questions . Kindly post next one…

Q: 4.5-5 Show that, for any 2-vectors a and b and any particular vector norm, J||a|| - ||b|| < |a - b||

A:

Q: If a set of vectors is linearly independent, then none of them is a linear combination of the…

A: We have to verify

Q: (a) Show that the vectors v = (0, 3, 1, – 1), vą = (6, 0, 5, 1), and v3 = (4, – 7, 1, 3) fom a…

A:

Q: Determine whether the vector b is a linear combination of a1, a2, a3. 2 a1 = |-2 a2 =|1 b = -1 az =…

A: Let us assume 'b' can be written as linear combination of a1; a2; a3 So, there exist scalars a, b…

Q: S is a linearly independent set,then for any x element of , x is not the linear combination of other…

A: Since, using the following definition of linearly dependent of sets-If a set of vectors is linearly…

Q: 2.11 Determine whether the following set of vectors is linearly independent: A = 2ê1 - ê2 + ê3, B =…

A: Sol

Q: 6. Determine if the vectors vi = (1,–1,3, –1), v2 = (1, –1,4, 2), v3 = (1, –1,5, 7) are linearly…

A:

Q: Can vector w = 3 be written as a linear combination of v₁ = 4 4 vector w belong to span{v₁,v₂}? V₂…

A: