Explain why S is not a basis for R2. S = {(2, 5), (6, 15)} O sis linearly dependent. O S does not span R2. O is linearly dependent and does not span R2.

Q: c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in…

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Q: Explain why the vectors U₁=(3, 8, -8) U₂ = (-12, -32, 32) form a linearly dependent set of vectors…

A: Linearly dependent vectors

Q: Determine whether or not the given vectors form a basis of R4 V1 %3D (-2, 6, 2, 4), v2 3D (1,0,…

A: To Determine: whether or not the given vectors form a basis of R4 Given: we have  v1=-2,6,2,4…

Q: {(1, 2, 3),(3, 2, 1),(0, 0, 1)}. Show that B is linearly independent and spans R3.

A: Linear span: Let V represent a vector space, and S=(v1,v2,...,vn) represent a subset of V. If every…

Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

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Q: 6. Consider the vectors u = (1,–2), v = (4,3), and w = (9,4). Find scalars k and k2 such that w =…

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Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

Q: Let B = (1, x, x², x*) be an ordered basis for P3. Find the coordinate vector of 8x – 6x2 – 9x + 3…

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Q: (a) (b) Any set of vectors containing the zero vector is linearly dependent. Any set of more than ʼn…

A: Let  be a sub set of  containing the zero vector               Then consider the following…

Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

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Q: 6. An n x n matrix A is diagonalizable if and only if it has n distinct eigenvalues. ? 7. Let W be a…

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Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: Show that the set S= {(-2,-4), (1, 2)} is the basis of R2 or not?

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Q: Is A = diagonalizable. Justify your conclusion. 10 120 -3 5 2,

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Q: Explain why S i not a basis for R?. S= {(5, 3), (1, 0), (0, 1)} O sis linearly dependent. O s does…

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Q: 9. Show that the following statements about two vectors (a, b), (c,d) = R² are equiv- alent. (a) ad…

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Q: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

A: It is an important part of statistics. It is widely used.

Q: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

Q: Which of the following sets is linearly independent? -ex-y-5=x+C OM= {(1,3),(3,9),(-1,-3)) M=…

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