2. Determine whether W is a subspace of V = C³ where W = {(0, b, c) E C3}

Q: (2) Find a basis for the subspace W = {(a+c,2a – 6, 3a – 26 – c, b + 2c) | a, b, c E R} of R4

A:

Q: Let S E M2x2; a = d and b +c = 0} be a subspace of Max2. %3D Then the dimension of S is equal to: O…

A:

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

A:

Q: 4) Show that the subspaces of R? are precisely {0}, R2, and all lines in R? through the origin.

A: A subspace of a vector space is itself a vector space that is contained in another vector space.

Q: Consider the subspace V of R4 given by 1 3 1 V = span || -1 1 1

A: Solution:-

Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find  The closest point y in the subspace W spanned by v1 and v2.

Q: (c) Find a subspace U such that R³ = W₁ OU.

A: C. Hint: Use the result of part (b) in the part (c) and obtain the required result.

Q: Let S = E M2x2; a = d and b +c = 0} be a subspace of M2x2- Then the dimension of S is equal to: 1 4

A: S=abcd∈M2×2; a=d and b+c=0 be a subspace of M2×2

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

A:

Q: Let Z E R³ | y Prove that Z is a subspace of R³. = Z

A:

Q: If S is a subspace of R", then so is the orthogonal complement of S.

A:

Q: 2.14. Prove that two subspaces V1 and V2 are linearly independent if and only if Vịn V2 = {0}.

A: V1 and V2 are two subspace.

Q: 1. Suppose that A is an nxn non-zero, real matrix and 2 is a fixed real number. Let E ={x=R* : AT =…

A:

Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

A:

Q: If V is a linear subspace of R", and x1 , ×2 , ... , Xn E V, then we must have span {x1, X2, Xn} =V.…

A: To determine that the statement, if V is a linear subspace of ℝn and x1, x2,....,xn∈V, then spanx1,…

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: Determine whether the following are subspaces of C[−1, 1]: The set of odd functions in C[−1, 1]

A: Consider the given set: C[−1, 1] Here the objective is to prove that the set of odd functions in…

Q: 3: Determine whether the following subsets are subspaces a) H = { ||zy = 0} CR". b) H = { x+ 2y + 3z…

A: We have to find

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

A:

Q: Prove that if S ⊆ R is a vector subspace of R, then either S = {0} or S = R.

A: Here, if s={0} then we are done.  But suppose that S⊂ℝ and S≠{0} is a vector subspace of ℝ to prove…

Q: 1. Determine whether W ER is a subspace of M. %3D b 2a

A: We have to determine whether W is a subspace of M22.   According top our guidelines we can solve…

Q: A base of the subspace W={ (a, b, c); a-2b+c=0} is:

A: According to the question,

Q: If W is a subspace, then ||projwv||² + ||v – projwv||2 = ||v|?.

A: Given W is a subspace of a vector space V. Now projWv denotes the projection of vector v onto the…

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

A: The solution is given as

Q: Let W = {a + bx + cx? +dx']c = a + b } be a subspace of P3. Then dimension of W is equal to: O 2 O 3…

A: To find the dimension of W.

Q: What is the dimension of w = {A € M2x2 (R) : A"| =ö} ĄT -2 1 2 This is not a subspace

A: W=AEM2×2(R) : AT1-2=→0  Let A=abcd, a,b,c,dER     AT=acbd     AT1-2=→0  ⇒acbd 1-2 =00 ⇒a-2cb-2d=00…

Q: Consider the subspace W = {(a, b, c) E R³ : a – 26 – 3c = 0} of R³. (a) Is {(5, 1,1)} a linearly…

A: (a) Yes. The detailed explanation is as follows below:

Q: and T are subspaces of V, then SUT

A:

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

A:

Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

A:

Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

A:

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R b)show that R° = F1…

A:

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: Show that S = {(a,0, b)"|a,b E R} forms a subspace of R³.

A: The solution are next step

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:

Q: Find a basis and the dimension of the subspace W = {(a+1)x+(2- )x²; a,b e R} of P,

A:

Q: 2. Determine whether the following subset S of R3 is a subspace or not. a) S = X2||x1x2x3 = X3 S.…

A: Let V be a vector space over field F. Let W be a subset of V then W is subspace of V over field F if…

Q: If S is a spanning set subspace of R* then the dimension of S must equal n. T F

A: The spanning set S , span the subspace of Rn .

Q: [M] Determine if y is in the subspace of R4 spanned by the columns of A, where -4 3 -5 -9 -8 7 -6 y…

A:

Q: Which of the following subsets of R is a subspace? {(:) \ z + y° = 0} {(:) \ +2y = 0} {(;) \ z +2y =…

A:

Q: Let S = {" E M2xzi a = d and b+c 0 be a subspace of M2x2. %3D Then the dimension of S is equal to: 4…

A:

Q: Given A be a 2 x 2 matrix with the form listed below: A = [0 a          b 0]  , where V = M2,2.…

A:

Q: 2. Determine whether W is a subspace of V = C³ where W = {(0,b, c) E C³}. %3D

A:

Q: 10 - What is the dimension of the subspace below? w = sp {C J. C 9 C 3 a) O 2 b) O 0 1 d) O -1 e) 3.

A: According to question  We have to calculate the dimension of the subspace.

Q: 1. Decide if the following subsets W C V are vector subspaces or not (justify) (a) W = x €RCR?. COs…

A:

Q: Let A and B be m x n matrices. Show that V = {x e R" : Ax = Bx} is a subspace of R".

A:

Q: Let W = {a + bx + cx? + dx*| a + b 0,c-a = 0, and d- 3a = 0} be a subspace of P3. Then the dimension…

A: