1 2 2 -2, u2 1 %3D 3 4.

Q: Using the Gram-Schmidt method, turn the basis B = dimensional subspace U C R³ into an ONB C = (c1,…

A: Given:     b1=111 , b2=-120 Gram-Schmidt method:        According to the gram-Schmidt process,…

Q: Is the set of all vectors (x, y) in R, with the usual addition and scalar multiplication, a subspace…

A:

Q: Suppose that U and V are both subspaces of R . Prove that their intersection U ∩ V = {v : v ∈ U…

A:

Q: Let U and W be subspaces of a vector space V. 1. Prove that UnW is also a subspace of V. 2. Must U…

A:

Q: find a basis for the given subspace of R3, and state its dimension. All vectors of the form (a, b,…

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: Find the standard matrix of the orthogonal projection onto the subspace W. Then use this matrix to…

A:

Q: Let u2 M = E R* : u; 2 0 for i = 1, 2, 3, 4 u = U3 U4 Is M a subspace of R*? Justify your answer.

A: Solution:-

Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: Let U1, U2, Uz be the following subspaces of R: Uj = {(a,b, c) : a = c}, Show that (a) R = U + U2,…

A: Answer

Q: The vector x is in a subspace H with a basis B= {b, ,b,}. Find the B-coordinate vector of x. 1 -3 -…

A: We will solve a system not equations to find the B-coordinate vector. The detailed solution is as…

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: Find the dimension of the subspace U={[a+c, b+c, a+2c+b] | a, b, c in R} Select one: a. 2 b. 4 c. 1…

A: We have given a subspace ,  U = a + c , b + c , a + 2c + b / a , b , c ∈ ℝ We need to find dimension…

Q: 6. Let U and W be 3-dimensional subspaces of a 4-dimensional vector space V, and suppose that U # W.…

A:

Q: Let A be an m × n matrix. Is the set W of all vectors x in Rn such that Ax = 0 a subspace of Rn?…

A: Set W of all vectors X in ℝn such that AX=0 is a subspace. Explain: Let X1 and X2 are two vectors…

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: - -{}}} {[:]} (a) Consider the subspace W = span 3 and consider the vector u = Find the vector w in…

A: Given that                      W=span23-1, 102 and the vector     u=1-1-1

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

A: According to the question,

Q: Let V be the vector space of all square sub-matrix over R. Examine whether or not W = (A: A E V, A²…

A: Let V be the vector space of all square sub-matrix over ℝ. Let , W = A / A∈V , A2 = A We need to…

Q: Find the standard matrix of the orthogonal projection onto the subspace W. Then use this matrix to…

A:

Q: If W is a subspace of R and v is any vector in R", then ||projwv|+|v-projwv||2= |v||2.

A: Introduction: Every vector that doesn't lie in a subspace can be uniquely expressed as a sum of two…

Q: Exercise 5. Give, for each of the following sets, a reason why it is not a vector subspace. 1. E =…

A: Zero vector must belongs to a vector subspace and vector subspace holds vector addition and scalar…

Q: Which of the following are subspaces of R°, if it is not explain briefly why not: (a) The zero…

A: As per guidelines, we will solve first three subparts only. We have to check which of the below are…

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: 2. Let W be the set of all vectors in R? whose first component is 2. Is W a subspace of R2? Justify…

A: It is not a subspace.

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: a Exercise 8. Find the dimension of the subspace W of R³ consisting of all vectors C such that a…

A: To find the dimension of the subspace W of ℝ3 consisting of all vectors abc such that a+b+c=0

Q: Given vector space V and W, is V a subspace of W?

A:

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: What is the formula for a projection of u onto d where d # 0? Find two different 2 x1 vectors u such…

A: We are only allowed to solve one question at a time and up to three sub-parts. So, we will answer…

Q: {] Find a basis for the subspace U = | a, b, c € R } of R³. Please justify your answer. -6

A:

Q: If u and v are vectors in R and W is a subspace of R with (u + V) belong to W, then both u and v…

A:

Q: For every two vectors u and v in R? the subspace spanned by {u, u + v} is the same as the subspace…

A: In this question,  We find linear span of the given vectors u and v.then check the equality with the…

Q: Let H be the subspace of R with basis B -2 and let x 6. (:) Is x a vector in H? 9. If x is in H,…

A: Given basis is B

Q: Find a basis for the subspace of R' that consists of all vectors perpendicular to both and 2 3

A:

Q: Let W be the subspace of IR' spanned by the vectors 1 4 -2 and -1 -7 Find the matrix A of the…

A:

Q: Given a Vector space V, if S is to be shown to be a subspace of V, is it enough to show that the…

A: Given a Vector space V, if S is to be shown to be a subspace of V, is it enough to show that the…

Q: 2 Indicate if the statement is True or False, and give a brief explanation why. a.A set of 7 vectors…

A:

Q: he zero vector in U is a subspace of V.

A: Inroduction a. Zero vector is a subspace of every vector space.

Q: In R, let S be the set of all vectors with third component 0. { a S = ER Show that S is a subspace…

A:

Q: Consider the vectors: V1 = (2,0,0,-2), |V2 = (–14 –7,–12,54). V3 = (0,1 1|-6) V4 =…

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: Find the closest point to y in the subspace W spanned by v, and v2. 1 - 2 - 1 1 2 y = V1 = 1 %3D V2…

A: The closest point to y in W is the projection of y on W.

Q: a . Is the set of all vectors of the form b, where a and b are any real numbers, a subspace W of R?…

A:

Q: A basis for the vector subspace: corresponds to? s = {(x, y, z) € R³ / x = 3y}

A:

Q: In Exercise , find the orthogonal projection of v onto the subspace W spanned by the vectors u?.…

A: Given :           v = 31-2 ; u1 = 111 ; u2 = 1-10   To find an orthogonal projection of v onto the…

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

A:

Q: Let W be the subspace of R spanned by the vectors 3 and -6 12 Find the matrix A of the orthogonal…

A:

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

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.