() S = and v = 3 1. Find the cosine of the angle between the first two vectors in S. 2. Find the length of the third vector in S. 3. Find the matrix of the standard inner product on W (obtained by restriction of the dot product on R') with respect to the basis S. 4. Orthonormalize S (Gram-Schmidt). 5. Find the projection of v onto W.

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A:

Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: The union of two subspaces of a vector space is not necessarily a subspace.

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Q: Use Axioms only to prove that the the solution to the equation 2x + y + 3z = 0 is a subspace of R³.

A: The given equation .To prove that the solution to the equation is a subspace of .

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

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Q: A subspace always contains the zero vector.

A: True Because of subspace is a nonempty set.

Q: What is a linear subspace?

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Q: Find an orthogonal basis for the subspace Span (1, 1 + x, 1 + x²) ≤ P3. Justify your answer!

A: Using the Gram Schmidt orthogonalisation process:

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…

Q: Is it possible to solve it using words like claim as my professor did in his example in other photo?…

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

A:

Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 19, Un 28 国 26 20 -2 -26…

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Q: 21 3 Find a basis for the subspace of R³ consisting of all vectors 22 such that 61 - 7x2 - 4x3 = 0.…

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

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Q: Sketch all four subspaces associated to mat 1 2 A = 3 6

A: Respected student, By Bartleby guidelines we have solved all the four subspaces with the first…

Q: Let V be the subspace of R spanned by v = . Describe V+ by finding a basis of

A:

Q: 3. Suppose W (a) (b) a = = {( 2 ): 9₂ Prove that W is a subspace of M2x2 (R). : a, b, c ER CER}.…

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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.