The vectors 4 -2 -2 2 12 -5+ k 4 are linearly independent if and only if k +

Q: 2. How many vectors does any basis of of Max(a+2)(R) contain, if a = max1<i<10 a;?

A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 - 4 4 9 - 3 + X3 3 %3D…

A: We will do this by using definition of augmented matrix

Q: If kk is a real number, then the vectors (1,k),(k,k+2) are linearly independent precisely when…

A:

Q: 14. The following vectors are the translation vector T and the spanning vectors X1 and X2, obtained…

A: We will use basic knowledge of linear algebra and Gaussian elimination to solve this question and…

Q: If the vector v= -8 can be written as a 9. 3 linear combination of v, and -3 V2 2 such that -3 v= a,…

A: The given problem is to find the value of a1 where vector can be written in the linear combination…

Q: -2 -4 -5 Let vi = -1 v2 = -3 , V3 = -4 and w = 4 1 2 3 5 1. Is w in {v1, v2, V3}? Type "yes" or…

A:

Q: Given trna -2 0. 1. -1 -4 0. 1 0 2 -1 -1 1 3 -2 write -4 as a linear combination of the vectors -1…

A: We want to write vector in linear combination of given vectors.

Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: 15 |ム=() -40 -30 -20 -10. -5 10 10 -10 15 (8)

A: We have,  x1=-5, 5 and x2=2,-2 This can be done as follows:

Q: Consider the following matrix and vector: 1 1 A = 1 -4 0 -3 -2 and x = 6

A:

Q: 4. Prove: If b is a non-zero vector, and x and x are both solutions to the matrix equation AX =6,…

A:

Q: [1] Construct a 3 x 3 nonzero matrix A such that the vector |2 is a solution of 3. Ах 3D0

A: A vector is given let x=123 To find: A non-zero 3×3× matrix,A=a11a12a13a21a22a23a31a32a33

Q: 3.2. Determine, if the vectors (9000 (:) (3) 1 1 1 1 1 1 1 1 are linearly independent or not. Do…

A: To determine a set of vector is linearly independent then determinant must be non zero.

Q: 1. If a set of vectors contains exactly 2 vectors and those vectors are scalar multiples of each…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R°…

A: System of Linear equations

Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: 7. The set of vectors: [0 1 -3 -1], [1 0 1 11, (11-2, 0] is linearly independent. Answer: yes or no

A:

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

A:

Q: Find a value of k such that the given vectors are linearly dependent [ -2 4+ k 4 ,X2 = 2 X1= ,X3 =…

A:

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: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

A:

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: 1) Determine whether the given vectors are linearly dependent or linearly independent. a)…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: The vectors -5 3 u = 16 v = -9 w = 11 31 3+k -23 are linearly dependent if and only if k = 3

A:

Q: 30. Prove: If A has linearly independent column vectors, and if Working with Proofs 30. Prove: If A…

A: To prove if A has linearly independent column vectors and if Ax=b is consistent, then the least…

Q: 6. a. Show that the vector á of b = (3, 1, 4) and ở = (1, 2, –3). (1, 12, –29) can be written as a…

A: We have to write the vector in the linear combination of two vectors

Q: The vectors 3 -4 u = -7 = 12 w = -8 -23 + k are linearly independent if and only if k #

A:

Q: If the vector v = v1 <=2 2 of v₁ = 05 2 -20 [E] -2 can be written as a linear combination -12 v=a1…

A: Substitute the vectors and then go ahead

Q: If the vectors 2 and are in the Null space of a matrix A. Then which of the following vectors may…

A:

Q: such that the vector 2 is a solution of 13. Construct a 3 x 3 nonzero matrix Ax = 0 123

A: I have construct a block matrix

Q: Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax = 0 is the line in R…

A: Given that Line passing through the points (5, 1) and the origin (0, 0) equation of line passing…

Q: Which of the following sets of vectors are linearly independent? or 12 4 -14 -2 6 22 -8 3 -21 2 O…

A: 1. 3 vectors in 4-dimensional space are always dependent. 2. Vectors are said to be independent if…

Q: 5. For which value of x do the following vectors form a linearly dependent set in ¹ X₂ G

A:

Q: 6. The set of vectors: [0 1 -3 -1], [101 1], [3 1 0 2], is linearly dependent. Answer: yes or no

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Suppose that Ax=b has no solution and the columns of A are linearly independent. Let t(A) denote the…

A: This is a problem of Linear Transformation.

Q: 5. For which real values of à do the following vectors form a linearly independent set in R³?

A: Solution; Consider the given vectors are: v1→ = λ, -12, -12v2→ = -12, λ, -12v3→ = -12, -12, λ Since…

Q: с pose the vector -6 is in the nullspace of the matrix d 6 -4 34 1 -5 23 1 -7 rmine c and d giving…

A: Topic:- application of algebra

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: The vectors -2 -4 u = -3 v = -2 w = -12 2 -1+ k 16 are linearly dependent if and only if k = 7

A: "Since you have asked multiple question, we will solve one for you. If you want any specific…

Q: 2.10 If A, B, and C are noncoplanar vectors (that is, A, B, and C are linearly independent),…

A: It is given that,  A, B and C are linearly independent vectors. We have to determine that whether…

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: For which vectors (b₁,b2, b3) do these systems have a solution? X1 b₁ 1 1 1 X1 HO-N-HD-B b2 and 0 1…

A:

Q: -5 5 4 -4 119 -5 3 -5 1 32 119 1 3 -4 5 -1 0 0 1 59 119 4 write 1 as a linear combination of the…

A:

Q: 1. Which of the following vectors is not a linear combination of and 3 1) |3)| [:] [:] 2) '4) 5) all…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: 1.36 (a) Show that any set of four vectors in R2 is linearly dependent. (b) Is this true for any set…

A:

Q: [1 Let A =0 3 -2 [1 7 4 2 For any vector b, find the complete solution Ax=b.

A:

Q: V; =[1 3 3 5]',V; =[3 10 6 7],V, =[2 7 3 2]' 7] , V, = [2 7 3 2]' are linearly independent.

A:

Q: 3) S contains only the vectors (-2+x-x² - 2x³), (4 + x - x² + 2x³), (8 + 5x -5x²+2x³), (10 + 7x -…

A:

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

A: Sol