Prove that every line through the origin in R3 is a subspace of R3.

Q: Determine whether W = {a + 2x + bx²|a, b = R} is a subspace of P2.

A: Explanation of the answer is as follows

Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: 2. Determine whether W = {a + br + cr?; a, b, c € R, a · b.c= 0} is a subspace of P2.

A:

Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: Find the basis of subspace defined as S = {(a, b, c)|a - b +2c=0}.

A:

Q: Show that the set            W={(a,b,c):a-3b+4c=0}  is a subspace of the 3-tuple space…

A:

Q: Determine if the subset of R3 consisting of vectors of the form [abc], where at most one of a, b,…

A: Concept: Subspace: A vector space that is a part of a bigger vector space is called a subspace. As a…

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

A:

Q: Prove that the subspaces of R3 are {0}, R3 itself, and any line or plane passing through the origin.

A: Let S be a subspace for R3   Hence,              If S is the subspace then by definition:…

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Show that W = {a + bx² € P₂|a, b = R} is a subspace of P2.

A: The solution is given as

Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}

A: We want to show that  U∩W≠{0}

Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

A:

Q: 3. Determine whether the set W = {(0,x2, 3, x4) : where x2 and x4 are real numbers} is a subspace of…

A: Subspace of a vector space

Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

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Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

A:

Q: Show that every subspace of ℝ is either {0} or ℝ.

A: Given: ℝ. To Show: Every subspace of ℝ is either {0} or ℝ.

Q: K = {at² + bt + c | a ≥ 0, b, c € R} ℃ P₂. S = {p = P₂|p(1) = 0}.

A: Find the basis and determine whether there is a subspace in these 2 subsets.   K=at2+bt+c | a≥0, b,c…

Q: Determine all subspaces of W.

A:

Q: Show that the set W is a subspace of M3x1 using the Subspace Test.

A:

Q: Determine whether W is a subspace of V

A:

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

A:

Q: Prove that span(S) is the intersoction of all subspaces of containing S.

A: Solution: Given that V is a space and S is a subset of V. Let Gs be the intersection of subspaces of…

Q: Prove that the set W= { | a,b are real numbers } is not a vector subspace of R3.

A:

Q: Find the basis and determine whether there's a subspace in the subset

A: To find the basis of K  and to check the subset S of K is subspace or not? For subspace we use the…

Q: Look for or create your own set W that is a subspace of R' or R.

A: We create a subspace of ℝ3.

Q: Show this subspace is a null space.

A:

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…

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.