a) Find all values of a so that polynomials f = 4t-a and g = 5t-6 are linearly dependent in P₁. Justify in details. ) Determine whether the set of all vectors y E] Justify in details. where z = y - 3x, is a subspace of R³.

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: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: Question 1 Let W be the set of all vectors of the form a) [α] b where -2a +6b-6c = 0 Lc -3 Determine…

A:

Q: b) Determine the values of x so that the following vectors are linearly dependent. (1 3 3 -6 -x.

A: Using determinant property of linearly dependent vectors,

Q: A subspace always contains the zero vector.

A: True Because of subspace is a nonempty set.

Q: Determine the real value/s of c such that the following vectors are linearly independent: 4 - 2 -6 6…

A:

Q: 2 3 Let vi V2 V3 2 and w = 3 2 a. Is w in {v1, V2, V3}? How many vectors are in {v1, v2, V3}? b. How…

A:

Q: s) Determine if these vectors for a basis for R³: linear combination of these vectors. 0·0-0--0- and…

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Q: c) Mark each statement True or False. Justify the answer. A subspace is also a vector space. • R? is…

A: Here , A subspace is olso a vector space: it is true.  R^2 is a subspace of R^3 : it is false.

Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: Let S be the space of all complex vectors (x, y, z) such that y = z². Determine whether or not S is…

A: In the given problem we verify the properties of vector addition

Q: Show that the set is linearty dependent by finding a nontrivial inear combination of vectors in the…

A: we have to show that the set is linearly dependent by finding a nontrivial linear combination of…

Q: Find all values of b for which the vectors are orthogonal 〈b, 3, 2〉,〈1, b, 1〉

A: Concept - If two vectors say u and v are orthogonal, then their dot product is equals to zero.That…

Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

A:

Q: Prove that the set ? = {(a + b, a -b): a and b are real numbers} is a subspace of ℝ2 with the…

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Q: Determine a basis for the vector space spanned by the vectors 3. V1 2 ,V2 .Vs 17 12 O A. {V1, V3,…

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Q: Let W be the subspace spanned by the u's. Write y as the sum of a vector in W and a vector…

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

A:

Q: Let W be the subspace spanned by the given vectors. Find a basis for WL. w1 = 1-18-2, w2 = 01-71…

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Q: 5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³…

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Q: Help find a basis for the subspace spanned by the given vectors provided attach. Whats the dimension…

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Q: Consider the following two sets of Euclidean vectors:

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Q: Describe the zero vector (the additive identity) of the vector space. R³ X

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Q: (i) Let {u, v} be linearly independent vectors in a vector space V. Determine whether set {v – u, v…

A: 7 (i) Given, u, v be linearly independent vectors in a vector space.

Q: Let V be the set of all ordered pairs of real numbers (x1, u) with u > 0. Consider the following…

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Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions