The vector x is in a subspace H with a basis B = (b, ,b2). Find the B-coordinate vector of x. - 1 , b2 - 19

Q: Find (a) a basis for and (b) the dimension of the subspace W of R4. W = {(2s − t, s, t, s): s and t…

A:

Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…

A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…

Q: 1. Determine which of the following sets of vectors are subspaces of R?. a) All vectors of the form…

A: According to our company guidelines we must do only three parts if multiple parts of the questions…

Q: Find an orthogonal basis of the subspace of spanned by the vectors 目目 。啡3, 。翻 3 -9 (а) (b) (c) -2…

A:

Q: Find a basis for the subspace of P2 spanned by the given vectors.  1 + x, x2, -2 + 2x2, -3x

A: Basis are (1, 1,0), (0, 0,1), (-2, 0,2), (0, -3, 0)

Q: Determine: If W = the set of all vectors in R2 whose second component is the square of the first. is…

A:

Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. 1 -3…

A: According to the given information, X is a vector in a subspace H with basis B. it is required to…

Q: Find a basis and the dimension of the given subspace of R4: a + c a – b b+c E R4 -a + b

A:

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: Find a basis for the subspace а : a, b, c, d E R with 3a + b=0 and c+ d = 0 C W = 6. 6. d of R4.

A: Since 3a+b=0 Therefore b= -3a  And since  c+d=0  Therefore d= -c

Q: For the given subspace, H, (i) find a basis for the subspace, and (ii) state the dimension. 2c (а) Н…

A:

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. The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. (a)…

A: We can solve this as follows:

Q: Find a basis for subspace S of M2,2. s ={ [ ] : 4a – b = 2c + 2d ; a, b, c, d E R - C

A: We have to find basis of subspace S of M2x2 matrix.

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: if W is the subspace spanned for the 3 vectors, find the sets that serve as a basis for W choices:…

A: The given vectors: v1=-1-75  ,    v2=4-59 ,    v3=69-1

Q: Given v = find the coordinates for v in the subspace W spanned by -7 u1 = and uz -1 -28 Note that uj…

A:

Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. %3D 1…

A:

Q: Find the closest point to y in the subspace W spanned by v, and v2. 11 9- -1 3. The closest point to…

A: concept:

Q: Find a basis for the subspace and state the dimension. {[ 2c a − b b − 3c a + 2b ]:a, b, c in R}.

A: The given subspace is 2ca-bb-3ca+2b. 2ca-bb-3ca+2b=a0101+b0-112+c20-30 Note that, the vectors…

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

A: According to the question,

Q: is in a subspace H with a basis B = {, 13: The vector x = Find the coordinate vector of x relative…

A: Write x as linear combination of basis linearly independent vectors and find coefficient

Q: Find an orthogonal basis of the subspace of spanned by the vectors 日目 4 (a) (b) (c) (d) 30 e.None of…

A:

Q: Find an orthogonal basis of the subspace of spanned by the vectors 日 目 3. (a) (b) (c) (d) 30 123 34

A: Find the orthogonal basis.

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

A:

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

A:

Q: The sequence B = (|1 3)) is a basis for the subspace U = {{ r2| |r1 – 3r2 + 2r3 = 0}. 13 The vector…

A: We have to find the coefficient for linear combination

Q: The vector x is in a subspace H with a basis B= {b,,b,}. Find the B-coordinate vector of x. 1 - 4 -…

A:

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

A:

Q: Find (a) a basis for and (b) the dimension of the subspace W of R4. W = {(s + 4t, t, s, 2s − t): s…

A:

Q: The vector x is in a subspace H with a basis ß= (b₁, b2]. Find the B-coordinate vector of x. -6-0-3…

A:

Q: The vector x is in a subspace H with a basis B = {b1, b2}. Find the B-coordinate vector of x. b1 b2…

A: The given basis is - β=[b1,b2]b1=2-24 ,b2=61-3 , X=410-22 To find β-coordinate vector of x.

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

A:

Q: a 6. Let H be a subspace of M2x2 whose vectors are of the form Then, B 2 is a basis for H. 7 Find…

A:

Q: The vector x is in a subspace H with a basis B = {b, b2}. Find the B-coordinate vector of x. - 3 2 2…

A: Coordinate of a vector

Q: Find a basis for the subspace 66 E R2x2 a, b E R of R2×2. 7a W 8а + 3b 4b Ex: 1 : 6 A basis for W is…

A: Given subspace of R2×2 is W=7a6b8a+3b4b, a,b∈R Then any element of W can be expressed as…

Q: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. 2 b1…

A: We have given the basis   B=b1,b2where b1=21 , b2=-13   and we have a vector x = 49in a subspace H…

Q: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. - 1 b1…

A:

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

A:

Q: Find the closest point to y in the subspace W spanned by v, and v2. 3 1 - 1 - 4 - 1 y = 1 1 ,V2 - 1…

A:

Q: Investigate the dimension of the following subspace of R*. All vectors of the form (a,b,c,d), where…

A:

Q: It can be shown (but you need not do so) that b 0 с d :]|++d} W = a +c= a subspace of M2.3. Find a…

A:

Q: In each part, find a basis for the given subspace of R4 (1) All vectors of the form (a, b, 0, 0).(2)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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: The sequence B = (3,5) is a basis for the subspace () -- V = { 22: 2xi + x2 – 13 = 0}. The vector w…

A:

Q: The vector x is in a subspace H with a basis B= {b,.b2}. Find the B-coordinate vector of x. %3D b, =…

A: Solution:Given b1 = 4-11 , b2 = -14 , x = 8-17let u,v be scalaris such that,x = ub1 + vb2⇒ 8-17 =…

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: Find the dimension of the subspace spanned by the given vectors. - 2 11 8 1 4 - 3 3 - 5 - 29 21

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.