O given and b, = are in vector R, %3D 3. Let w= span { bisba s. Is the set w a Subspace of R2? Justify your answer.

Q: Let S = i. ii. iv. [2s- - S s,te R t Inter} -S Show that S is a subspace of R4 Find two vectors that…

A:

Q: Is W a subspace of the vector space V? Justify your answer. 1. Wis subset of V = R3 where a W = {…

A: I just used a test of subspace to check the W is subspace

Q: 3. Let W = {(x,y,z): x? + y? = z}. Is W a subspace of V = R3? %3D

A: We need to check if W is a subspace or not.

Q: Show that U= {(x, y, z): r, y = R} is a subspace of R³. Then, find a linear complement of U in R³.…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (a) find the orthogonal complement S⊥, and (b) find the direct sum S⊕S⊥. S is the subspace of R3…

A:

Q: What is the dimensionality of the subspace spanned by V = \v +7w for the following v, w? a) b) d) 12

A:

Q: a a subspace of R³? Show your proof. La+2b] the set of vectors of the form

A: Given the set of vectors of the form aba+2b , which can also be expressed as:             W =…

Q: Q. 5 If V is any vector space, show that (0} and V are subspaces of V.

A: We have that V is a vector space.  Now, V is said to be a vector space over a field F along with 2…

Q: "The set U = {(x, y, z, w) E R* | ¤ – y = z + 2w and r + y – z = w + 1} is a subspace." %3D

A: U=x,y,z,w∈ℝ4|x-y=z+2w and x+y-z=w+1 To find: U is a subspace or not Take x,y,z,w=0,0,0,0 Then,…

Q: , dim W 5. Let U, W be subspaces of a vector space V. If dim U and Un W = {0}, what is dim (U+ W)?

A: Let V be a vector space over a field k and let U, W be finite-dimensional subspaces of V.  Then…

Q: 14. Let V = R°and W = {(a, b, c) E Vla² + b² = c²}. Is W a subspace of V? If so,what is its…

A:

Q: The shape's vector set is a subspace of R3

A: solution :-

Q: a Q#01:- Let W be the set of all vectors in R3 of the form where a and La + b! b are any real…

A:

Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

A:

Q: Let V be a subset of Rª. Recall that the span of any set of vectors is a subspace. What is the…

A: Given V=1000,1100,1110,1910 subset of ℝ4 To find the dimension of span(V)=?

Q: Let X =R, and M = (0} , the M is not subspace of R O True O False

A: Subspace of a vector space

Q: R! Consider Hhe veetors and () How many vectors are in span {v, v } ? (6) Is the Hectay w in Hhe…

A: Span of vector means collection of all possible linear combination of those vectors.

Q: a Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

A:

Q: i) Determine whether or not the set w - ((x.y.2) ej+y +-1) is a subspace of w i) Write (1,7,17) as a…

A: W is not subspace because (0,0,0) does not belongs to this set  ( 0^2 + 0^2 + 0^2 is not equal to 1)…

Q: If S is a subspace of R* and dim(S) = 3, what is the dimension of the orthogonal complement of S?…

A:

Q: Let W = (a + bx + cx? + dx³la + 2c 0 andb-d D 0) be a subspace of P,. %3D Then dimension of W is…

A: Given  W={a+bx+cx2+dx3| a+2c=0 and b-d=0}Since a+2c=0⇒a=-2cand b-d=0⇒b=dwhich gives…

Q: Consider the set S = {(x, y, z) ∈ R3 | x - 2y = z}. (a) Show that S contains the zero vector. (b) Is…

A:

Q: In each part, find a basis for the given subspace of R3, and state its dimension. a) The plane 2x −…

A:

Q: Let W be the set of all vectors in R³ of the form a B b where b = 2, a is any real number and c < 0,…

A:

Q: Determine whether U = {(1, s, t)ls,t e R} is a subspace of R.

A: FOR ANY SUBSET U TO BE A SUBSPACE OF ANY VECTOR SPACE V IT IS NECESSARY THAT U HAS ZERO VECTOR IN…

Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

A:

Q: Which of the following is the dimension of the subspace W = :y = x+z and x, y, z, w e R} CR ? (a) 0…

A:

Q: Determine whether or not the given set W is a subspace. W = {T E R" | AT = 23 – B }, where A, B are…

A: We will use the definition for a set to be a subspace to check whether the given W is a subspace or…

Q: -아 Select the correct statements for W = E R²| 4x1 + 3x2 The zero vector is in W If u, v e W, then u…

A: We have to choose the correct statement for…

Q: Consider the subspace S = {(7a5b)|a,b € R} Then the dimension of S corresponds to?

A:

Q: . Let u = 6 6 " and let W be the set of all x in R3 such that u x = 0. (a) Show that W is a subspace…

A:

Q: Let W be the set of all vectors of the form Na subspace of R³ 0 2

A: Here given that  vector  [a 0 2]    We know that condition of subspace  w is zero vector belong…

Q: Which of the following is the dimension of the subspace W = y :y = x+z and x, y, z, w E R C R* ? (a)…

A: The option (d) is true.

Q: The answer above is NOT correct. Find the orthogonal projection of 20 onto the subspace W of R…

A:

Q: a Is the set of vectors of the form La+2b] subspace of R3? Show your proof. a

A:

Q: . Let W be the subspace of R3 spanned by the vectors vj=(1,0,7), v2=(6,1,7), and V3=(14,-1,13). Find…

A:

Q: Consider the set ? = ((x, x+ y, 2y)|x,y are real) of vectors in r3 . Is W a subspace? If yes, prove…

A: We have Set S = {(x, x + y, 2y) | x, y are real}. Let u, v be any two element of S then,

Q: а о if v = M22 ( R) and W = { : а , bE R } 0 a then .a W is not subspace of .b W is subspace of

A:

Q: Verify that U1 = {(x, y) E R² : y = -2x} is a real vector subspace of R?. hat U2 = {(x,y, z) E R³ :…

A: This a question of linear algebra and vector space.

Q: - Let V = R and W = {(a, b, c) E V \a + b = c}. Is W a subspace of V? If so, what is its dimension?

A:

Q: Let W be the subspace spanned by u, and u2, and write y as the sum of a vector in W and a vector…

A:

Q: a+b |a, b, c e R) of My? a +e 6- a каn C? b-c ,каn C What is the dimension of the subspace U kan Ç О…

A:

Q: Let U = a :a ERis a subspace of R? | 2a Is U a subset of R2? Is 0 E U?

A:

Q: (A) Let U1, U2, U3 be subspaces of M2x2(R). If V = U1 e U2 e U3, then dim V = 4.

A: So,  V is the direct sum of the subspaces U1, U2, U3  of M2×2(R) , i.e. dim(U1) = dim(U2) = dim(U3)…

Q: {}]*+*s} {:x² + y? < 1} is a subset of R2. Show Question : The set H = %3D that H is not a subspace…

A: In the given question we have to show that the set H is not a subspace of . Concept: Here we use a…

Q: Let U and WW denote subspaces of R", and assume that U C W. If dim U = n - 1, show that either W =…

A:

Q: Show that U = {(r, y, z): r.ye R} is a subspace of R³. Then, find a linear complemen

A: Here a subset of ℝ3 is given as U=x, y, x: x,y∈ℝ

Q: Let Uz?la :a,bE R and :c;d eR be two Subspaces of M, CR). Show that U eW= M, IR).

A:

Q: What is the dimension of the subspace below? w = sp { J. C a) O 0 b) c)O 2 d) O 3 e) O -1 1,

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.