a + 2b a + 1 3. Is H = a subspace of R? Why or why not? a

Q: Let the set {v,, v2} be linearly dependent. Determine whether the set {v, + 4v,, 5v, - v2} is also…

A:

Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

A:

Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: Find a non-zero vector in the column space of A. A = -8 4 -20 12 -25 -4 -6 -5 24 0 30

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: Given 7 = find the closest point to in the subspace W spanned by -2 and -3 -1 30

A:

Q: 11. Explain why the subset of R² shaded below is not a subspace of R². 3 1 -3 -2 -1 -1 -2 -3 12.…

A: I have given the details below

Q: -3 6. -1 1 6. Let B = 1 -2 -11. Determine a basis for, and dimension of, the following -4 8 -4]…

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Q: Find the dimension of the subspace spanned by the given vectors.

A:

Q: Let V₁ = [], , V3 Determine if the set {V₁, V₂, V3} is linearly independent. ‚ V2 =

A: Definition of linearly independent set

Q: Section B: Determine of the following set W is subspace of V=R³: W-{(a, 1, 1): a ER).

A: We have to determine whether the set W is a subspace of V=R3.…

Q: Given 7 - -6 -8 -8 find the closest point to in the subspace W spanned by 5 -6 -2 and -6 3 3 -54

A: We have to find the closest point to the vector v in the subspace spanned by the vectors x and y…

Q: 2. Let W= = {(x³-5, y-1,z²+4) € R³|x, y, z E R}. Is W a vector subspace of R³? Justify your…

A: A vector space is a fundamental concept in linear algebra, and it provides a mathematical structure…

Q: 6. Is the following a subspace? Show/prove which step fails. {x e R? : x1 + x2 = 3}

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Q: 1 1 -1 |1– 5k + k² 1+4k 1– 2k 3 -2 1

A: we can write the given vectors as a linear combination of vectors…

Q: 5. Which of the following sets of vectors in P2 is linearly dependent? A. {1,x, x²} B. {1+x,1 – x,2}…

A: If a vector can be written as linear combination of other vectors in the set then that set of…

Q: 14) Find all values of h such that y will be in the subspace of 3 spanned by v1, v2, v3 if vị = 2,…

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Q: What is a vector space axiom?

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Q: 3. (a) Let W = {a+bx + cx² : ac= 0} C P2. Is W a subspace of P2? Justify your answer. (b) Let V = {a…

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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.