Determine if y is in the subspace of R4 spanned by the columns of A. -5 15 -6 -9 7 -7 -8 A = 6 13 y = - 14 -8 2 -4 3 -3 -9 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The vector y is in the subspace spanned by the columns of A because y can be written as a linear combination of these columns as follows. -5 15 - 6 -9 -8 13 7 -7 6 14 -8 2 - 4 -3 -9 (Type integers or simplified fractions.) O B. The vector y is not in the subspace spanned by the columns of A

Q: Determine whether the statement is true or false. R¹ is a subspace of R¹7 False

A:

Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

A:

Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: Given = 2 2 -6 3 6 1-0 and -6 36 find the closest point to in the subspace W spanned by

A: Given,        To  find the closest point to v in the subspace W spanned by

Q: A subspace always contains the zero vector.

A: True Because of subspace is a nonempty set.

Q: Find a basis for the subspace of P2 spanned by the given vectors.  1 + x, x2, -2 + 2x2, -3x

A: Basis are (1, 1,0), (0, 0,1), (-2, 0,2), (0, -3, 0)

Q: Determine; if W = the set of all odd functions is a subspace.

A:

Q: 3. This problem is about set addition and subspaces. Let di and d2 = span{di}, %3D 1 U = span{d2}.…

A: Sum of two subspace

Q: Only use the definition of subspaces, determine whether U = {(-a,–2B+a,a – 3,)| a ER and ß E R} is a…

A:

Q: Given 7 = find the closest point to in the subspace W spanned by -2 and -3 -1 30

A:

Q: 2 -1 3 -1 -3 -2 -1 -6 -7 2 4 -8 6. Find bases and dimensions for the four subspaces associated with…

A:

Q: Find the dimension of the vector space.P7

A:

Q: Why isn't R2 a subspace of R³?

A: For being a subspace a space must be a subset of the other. But here R2 is not a subset of R3. So…

Q: 13. Find a basis for the subspace spanned by the vectors What is the dimension of the subspace? C100

A:

Q: Determine if v is in the subspace of P3 given by span{x + x - 5, x2 + 2x + 1, x-x2 + x}. v = x? + 2x…

A:

Q: P = {ax? + bx +c€ P2/ a + 3b = 1- c} %3D Q = {ax? + bx +c € P2/ 2a + 3b = -c}

A:

Q: v1 Determine if the subset of R consisting of vectors of the form where v1 - v2+ v3 – v4 + v5- - Un…

A:

Q: Given 7 - -6 -8 -8 find the closest point to in the subspace W spanned by 5 -6 -2 and -6 3 3 -54

A: We have to find the closest point to the vector v in the subspace spanned by the vectors x and y…

Q: Let v₁ = O 1 5, V₂ = No Yes -2 -7 13 and w= - 3 -6 19 Is w is in the subspace of R³ generated by v₁…

A:

Q: Determine whether the sets S₁ and S₂ span the same subspace of R³. S₁ = {(1, 2, -1), (0, 1, 1), (2,…

A:

Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

A:

Q: Given 7: -9 -10 0 find the closest point to in the subspace W spanned by -5 -6 -4 and 64

A: We have to find out the closest point of  in the subspace W spanned by Here noted that ,let,So…

Q: Mark each statement True or False. Justify the answer. A subspace is also a vector space. R2 is a…

A:

Q: Find the dimension of the vector space.P4

A: Here the given vector space V= P4 or

Q: Determine whether b can be written as a linear combination of a₁, a₂, and a3. In other words,…

A:

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

A:

Q: 2. Determine whether each set described is a subspace or R2. Justify your answer. H (a) The set of…

A:

Q: 14) Find all values of h such that y will be in the subspace of 3 spanned by v1, v2, v3 if vị = 2,…

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.