Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1} a subspace of R*? Show the details of %3D your argument.

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: Find the dimension of the subspace H of IR2 spanned by the vectors and

A:

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

A: Solution:-

Q: Let W - (a + bx + cx + dx'l a +b-0 and c - 3d = 0) be a subspace of Py. Then the dimension of W is…

A:

Q: Let W = {a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to O…

A:

Q: The dimension of the subspace W = {A E R™Xn: A is diagonal} is 2. balg j

A: Dimension of the subspace:          If V is spanned by a finite set , then V is said to be finite…

Q: Is W = {(x, y, z, w) | 4z – 2y = 3w – x & y+ z = -2x} a subspace? Justify your answer. If it's a…

A: Given W=x,y,z,w:4z-2y=3w-x & y+z=-2x

Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

A:

Q: Let W = {a + bx + cx + dx| a+ b = 0 and c – 3d = 0} be a subspace of P3 Then the dimension of W is…

A: Linear combination of vectors we use to find.

Q: Let V = {ax* + bx² + c : a, b, c E R}. Is V a subspace of P4?

A:

Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

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: Explain why this statement is true: If V is a subspace of Rn, then there is a n×n matrix A such that…

A: To Proof :-  If V  is a subspace of Rn , then there is a n × n  matrix A such that V = Col A.

Q: 10. Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R³? Justify. (b) Is Y a vector space? Justify.

A:

Q: Find the orthogonal projection ŷ of y = onto the subspace W = Span { uị u2 5 Ex: 1.23 : ŷ =

A:

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

A:

Q: For an m x n matrix A, the column space is a subspace of Rn. True False

A:

Q: What is the dimension of the subspace W = {A = [aij] € R4x5|a45 = 0} dimW = Ex: 5

A:

Q: Let W {a + bx + cx2 + dx³| a + b = 0 and c - 3d = 0} be a subspace of P3. %3D Then the dimension of…

A:

Q: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

A:

Q: Let W = (a+ bx + cx² + dx*| a +b= 0,c-a = 0, and d-3a = 0) be a subspace of P. Then the dimension of…

A: The dimension of the vector space of polynomials in x with real coefficients having degree at most .

Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?

A: Subspace

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: 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: Suppose that U cr|xyer F4 y EF, U is a subspace of F4- you don't have to! Find a subspace V of F4…

A:

Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

Q: What is the dimension of the subspace H of R? spanned by 2 -4 4 32- :? -5 10 -10 O A) 0 O B) 3 O ) 4…

A: The number of vectors in a basis of a vector space is said to be the dimension of that vector space…

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

A:

Q: Give a counter example to show that W is not subspace of R³. W=set of (x, y, z) where x + y = 1 6. ,

A:

Q: a b Show that W |a,b ER} is a subspace of M2x2. %3D -b a

A:

Q: 1. Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1) a subspace of R*? Show the details of %3D your…

A:

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

A:

Q: Let W = {(x, y, 1) | x, y, E R}. Is W a subspace of R3?

A:

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

A:

Q: Consider the set S = y ER : 3x – 5y = 0, x + z =- . Is this a subspace of R ? Explain why or why…

A: Given set is S=xyz∈R3:3x−5y=0, x+z=4. We have to check whether the set S is the subspace of R3 or…

Q: The set of all points in R3 satisfying x + y - z = 0 is a subspace. Note that the set of point…

A: It is known that any subspace of ℝ3 should contain an additivities identity element 0, 0, 0.

Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0} W= {(x,y,z): x2 + y2+ z2…

A: The given vector space is R3. We know that a subset W of a vector space V is a subspace of V if it…

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: ) The degree of pa is equal to the dimension of the cyclic subspace Z (a ; T) .

A:

Q: Find the dimension of the subspace W of R4 spanned by S = {v1, v2, v3} = {(−1, 2, 5, 0), (3, 0, 1,…

A: Dimension of a subspace W is given by the number of linearly independent vectors in the basis of W,…

Q: Find the orthogonal projection ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

A:

Q: Is Q = {(x,y,z) | x=2y & z=1} a subspace of R?

A:

Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

A:

Q: Let W = (a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of Py. Then the dimension of W is equal to

A: Here we will find out dimension of W.

Q: Show that points on the plane x-2y+4z=0 form a subspace of R3

A:

Q: Let W = {a + bx + cx2 + dx³| a +b = 0,c - a = 0, and d - 3a = 0} be a subspace of P3. Then the…

A: We have to check

Q: Explain why S = {(r,y) : x, y € R, x > 0} is not a subspace of R²

A:

Q: Let W = {a + bx + cx2 + dx³| a + b = 0 and c – 3d = 0 } be a subspace of P3. Then the dimension of W…

A:

Q: Q2. Check if the following points lies on the subspace U spanned by the vectors = [2 -1 2]', x2 = [0…

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: