What can be said about Nul A if A is a 5×7 ​matrix? Could it be the zero​ subspace? Why or why​ not?

Q: Is the union of two subspaces of a vector space, a subspace.

A:

Q: a 2. Is the set of vectors of the form a subspace of R? Show your proof

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

Q: Determine whether the subspaces are orthogonal.

A:

Q: Let v1=[ 1 0 −1 ], v2=[ 2 1

A:

Q: Find a basis for the subspace of Rª spanned by S. S = {(2, 9, -2, 53), (-4, 2, 4, –2), (8, –4, -8,…

A:

Q: Find a basis for the subspace of R3 spanned by s. S = {(1, 5, 9), (-1, 6, 9), (2, 6, 1)}

A:

Q: Suppose U and W are subspaces of V for which UUW is a subspace. Show that UCW or WCU.

A:

Q: Give an example of a non-zero subspace of R^4 which has dimension > 1 and does not contain any of…

A: Consider the example f(x) = {2 + x + x2}, this given polynomial has dimension 3 with the basis {1,…

Q: What is a linear subspace?

A:

Q: (() 2 6. Are the two subspaces span and span (() orthogonal? Justify your answer.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The set of all nxn matrices whose entries are negative or zero is a subspace of Mnn: True False

A: The answer is true

Q: Show that (a,b,c) where c=a+b is subspace of R3

A:

Q: Determine if W is a subspace of R³, and show why or why not

A: In this question, we have to check the given set is subspace or not

Q: Prove that the set ? = {(a + b, a -b): a and b are real numbers} is a subspace of ℝ2 with the…

A:

Q: If S and T are subspaces of V, then SNT is a subspace. Select one: True False

A: Since this is a true or false question we can come directly into the solution without going into the…

Q: What is the dimension of the following subspace U of R2x2 ? 3 U = span({ }) -2 -2

A:

Q: Find the dimension of the subspace spanned by the given vectors below. 4 6. -5 8 -4 O 3 O 4

A:

Q: Find bases for the four fundamental subspaces of the matrix A.

A: Given,

Q: In R4 , find the dimension of the subspace spanned by the vectors {(1, 1, 1, 1)T , (1, 2, 2, 2)T ,…

A: Given vectors are {(1, 1, 1, 1)T , (1, 2, 2, 2)T , (1, 1, 2, 1)T , (2, 2, 3, 2)T , (4, 5, 6, 5)T }.

Q: Find a linearly independent set of vectors that spans the same subspace of R* 4 as that spanned by…

A:

Q: If S and T are subspaces of V, then SUT is a subspace. Select one: True False

A: Given S and T are two subspacewe have to check whether S∪T  is subspace or notClearly  S∪T  is…

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

A:

Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 4, 7), (-1, 5, 7), (2, 5, 1)}

A: The matrix form the vectors is: A=1-12455771

Q: If V is infinite-dimensional and S-is an infinite-dimensional subspace, must the dimension of V/S be…

A:

Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

Q: Let ū be some fixed vector in R" and let S be the set of all vectors in R" that are orthogonal to ū.…

A:

Q: Show that W = {(a, 0, b)la, b = R} is a subspace of R³.

A: As per guidelines we are supposed to solve the maximum first questions only .kindly post another…

Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

A:

Q: Provide a situation in where it shows a union of two subspaces of a vector space V and is not…

A:

Q: Explain why the subset а — b S = a +b а,bER -26 – 3a of R3 is or is not a subspace of R³.

A: Given subset of R3 is  S={a-ba+b-2b-3a|a,b∈R} explain if S is subspace of R3

Q: determine the dimension of the subspace of R3 spanned by the given vectors.

A:

Q: Explain why the subset а —b S : a + b а,b€ R -2b — За of R³ is or is not a subspace of R³.

A:

Q: (a) Consider a system Ax = b. If the system is consistent, which fundamen subspace of A contains b?…

A: Solve the following

Q: Suppose W is a subspace of Rn spanned by n nonzero orthogonal vectors. Explain why W = Rn.

A:

Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

A:

Q: Determine whether W = {ao + a1x + a2x² + a3x°|ao + a2 = az ɑ1} is a subspace of P3.

A:

Q: Given a Vector space V, if S is to be shown to be a subspace of V, is it enough to show that the…

A: Given a Vector space V, if S is to be shown to be a subspace of V, is it enough to show that the…

Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

A:

Q: Give example of subspaces of land l?wich are not closed.

A:

Q: Find a linearly independent collection of vectors which spans the following subspace of R4: 2 3 -3…

A:

Q: are subspaces of R ?

A:

Q: Find the dimension of the subspace Hof R2 spanned by

A:

Q: Determine the dimension of the subspace H, where H = -6

A:

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 5, 7), (-1, 6, 7), (2, 6, 1)}

A: Write the given set of elements as the rows  to form a 3x3 matrix. The space spanned by the rows of…

Q: Why are [0,∞) and (0,∞) which are subspaces of the real number system with the usual topology not…

A:

Q: If A has the same four fundamental subspaces as B, does A = B?

A: Four Fundamental Subspaces: Let be a matrix of order and be its transpose matrix. Then The row…

Q: is a subspace of M23-

A: A nonempty subset W is a subspace of a vector space V if, whenever w1, w2 are elements of W and α is…

Q: Suppose U and W are subspaces of V for which UUW is a subspace. Show that UCW or W CU.

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.