B. Let V be P2 with the inner product given by evaluation at -2, -1, 0,1 and 2. Let p1(t) = 2t + 3, p2(t) = 2t2 - t and p3(t) = 3t2 + 1. Find the orthogonal projection of p3 onto %3D the subspace spanned by p1 and p2.

Q: a) Find all values of a so that polynomials f = 4t-a and g = 5t-6 are linearly dependent in P₁.…

A: We can find the value of 'a' for which the given polynomial is linear dependent.

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A:

Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

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: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

A: Given :           Three vectors that spans of ℝ3 as :                  v1 = -23-2 , v2 = 480 , v3 =…

Q: O Linear subspace L is given by the equations 2r1 + r2 + 3r3 - 14 = 0 = 0 3r1 + 2r2 – 2r4 3r1 + 12 +…

A: Let AX=0 213-1320-2319-1x1x2x3x4=000R2→R2-32R1 , R3→R3-32R1…

Q: Let v1=[ 1 0 −1 ], v2=[ 2 1

A:

Q: Find a basis for the indicated subspace of R³. The line of intersection of the planes with equations…

A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

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A: First we have to construct a 2x3 matrix of rank 1. then find the vector in the subspace (row space…

Q: H = 1 -3 2 -4 Determine the dimension of the subspace H, where 7 9 -6 12 2 -1 4 2 5 - -3 7

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A:

Q: State the dimension of the following subspace, The solution space {(a,b,c): a-3b+c=0, b-2c=0,…

A: We have to find the dimension of the subspace.

Q: Find the closest point to y in the subspace W spanned by V₁ and V₂ 2 2 - 1 y= a. 3/6 -2/6 丽··· -1/6…

A:

Q: What is a linear subspace?

A:

Q: Let W be the subspace spanned by the vectors (1,2, 0, 3) and (2, 1,3,0). Find : a basis for W+.

A: Given that W is a subspace spanned by the vectors 1 , 2 , 0 , 3 and 2 , 1 , 3 , 0 . i.e., W = span1…

Q: 3. This problem is about set addition and subspaces. Let di and d2 = span{di}, %3D 1 U = span{d2}.…

A: Sum of two subspace

Q: yes, hi. I've seen another source, use set variables to 0 and then solve individually, answers are…

A: setting z=0 and solving for x and y. similarly setting y=0 and solving for x and z.

Q: Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: The given vectors are                                   -3110, -12613, 3-55-6, -33-23…

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A: We have to find the orthogonal projection of the vector  onto the subspace of  spanned by  and .

Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

A:

Q: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W. Show that V ∩W…

A: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W.  We have to…

Q: Q2. Let V = {(a, b, c, d) : b + 2c + d = 0} and W = {(a,b, c, d) : a + 2b = 0, c = 5d} be two…

A:

Q: Is R2 a subspace of the complex vector space C²? Justify your Yes/No answer.

A:

Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

A:

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Q: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

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Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

A:

Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: The given subspaces of ℝ4 are U1={a, b, c, d) ℝ4| 1b=с; a=d=0};   U2={(a, b, c, d)  ℝ4| a - b + 2c +…

Q: The set of all vectors in R squared  that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy  3x+4y=1  is not a subspace of R squared.  i.e.…

Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

A:

Q: Find the coordinate vector of v = with respect to the basis -000 1 for the subspace of R4 spanned by…

A:

Q: (a) Determine whether the set of all vectors of the form (a,b,c), where b= a+c, is a subspace of R³.…

A: Consider the subset S of ℝ3 defined as, S=(a,b,c)∈ℝ3 | b=a+c Take  a1,a2,a3,b1,b2,b3…

Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: As per bartleby guidelines for a question only first three sub questions has to be answered please…

Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

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: Find a basis for the subspace of R4 determined by the equation 2x-3y+4z w = 0

A:

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

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.