The set W = : 3x - y = z - 5w = 0 %3D is a subspace of RT. What is the dimension of W Select one: а. 2 b. 4 С. 1 d. 3

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…

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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…

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Q: Let X = 1 ,and let V = {A E M2(R) | AX = XA}, a subspace of M2(R). 0. Find a basis for V, and write…

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

A: Solution:-

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: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

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Q: Find a basis for the given subspace of R° , and state its dimension for the plane 4 x - 2 y + 5 z =…

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Q: For which value of t is the set V below a subspace of R3? V = {(x, y, z) | 5x + 15y = 16x + 3y + 19z…

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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: Find the closest point to y in the subspace W spanned by v1 and v2 1 ,V2 = 1 y = V1 = -3. I • E 2 b)…

A: Here we have to find the closest point to y in the subspace W spanned by v1 and v2 .

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

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Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…

A: To find The closest point to y in the subspace w spanned by u1 and u2

Q: Which of the following sets is NOT subspace of IR? 2 Span -5 {8} Г1 2 31 The set of solutions to the…

A: solve the following

Q: to the subspace W = Span{u1, u2} where 0. Find the distance from the vector y and u2 = -2 O 2 01

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Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 17, U₁ 2, U₂ = 0-16 16 24 31…

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

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Q: S= {[a b c]e R³|b= 3a and c = a +3} is a subspace of R' %3D ylgn O ihi O

A: To check whether S=a b c∈ℝ3|b=3a and c=a+3 is a subspace of ℝ3

Q: Which of the following sets is NOT a subspace of R'? {E} [1 Го 2 31 The set of solutions to the…

A: Following sets are given

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

A: Since you have asked multiple questions, we will solve the First Question for you. If youwant any…

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: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

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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: Find the closest point to y in the subspace W spanned by vị and vz 2 y =| 1 ,v1 0,v2 -2 2 а) b) c)…

A: The following is the solved answer.

Q: Determine whether W is a subspace of V = C, where W = {(0, b,c) E C³

A: V=ℂ3 and W=0,b,c∈ℂ3

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

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Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: Which of the following is a subspace of p2? O a. R2 x, e R W = Зх, + 1 1. Ob. W = ER| x*2 2 0 C. ER?…

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Q: ind the closest point to y in the subspace W spanned by vị and v2 2 y =| 1 |,v1 = ,V2 = |-2 2 а) b)…

A: We will use the following method.

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

A: 1 is the answer.

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

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Q: Find the closest point to y in the subspace W spanned by v1 and v2 -21 1 y = | 2 = 2,v2 l1. -1 1 0.…

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Q: What is the dimensionality of the subspace spanned by V = Av +yw for the following v, w? 2 4 a) b)…

A: See the attachment

Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

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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…

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

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Q: Let W = {(" ): a + 2c = 0 and b-d = 0} be a subspace of M22. Then dimension of W is equal to: 4 2…

A: We know that  dim W = number of elements in basis of W  If S is basis of W then i) S is linearly…

Q: Find the closest point to y in the subspace W spanned by u, and u2. 7 2 y = 21 u1 2 , u2* 3 38 - 1 4…

A: Given that     y = (7,21,38) , u1 = (2,2,-1) and u2 = (-1,3,4) Here we have to find the closest…

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: 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: Find the closest point to y in the subspace W spanned by v1 and v2 y = | 1 -3 V2 = -2 а) b) 2 c) 1…

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Q: Let S= +c = 0 be a subspace of Mzxa- Then the dimension of S is equal to: 2.

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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…

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Q: Show that the solution set to a system of equations of the form au*, + Azyš, + + a, x = 0 Inn + ar =…

A: The given system of homogeneous linear equations is equivalent to a matrix equation of the form: Ax…

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

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Q: Which of the following sets are subspaces of Rª ? I. The solution set of the system Ar = 0, for a 4…

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

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: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…

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

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Q: Find the closest point to y in the subspace W spanned by vị and vz 2 1 y =| 1 |,v1 =| 0 [0] 2 lo] 2…

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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.