Consider the basis B = } |0|, -- a. Find the coordinates of the vector i = | 1 rela b. Consider the linear transformation T: R3 R3 i

Q: Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent.

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Q: Are the vectors u = (-3,0,2), v = (-2,-3,0), and v= (-16, -15, 4) linearly dependent? if yes, find a…

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: Write N(A) as the span of a vector (r vectors). What is dimN(A)? Why?

A: Null space, N(A) is the set of all vectors x in R^4 here, which are solutions of the equation Ax=0,…

Q: Let m = (-3,1,5) and n = (5,-1,2). calculate the vector p = n - ((m*n)/(m*m))*m.

A: here we get p=0

Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: V₁ = V1 V3 = V2= 4 [ 3 [-1] 2 3]

A: We use the properties of linear combination to

Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

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Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: Find the orthogonal projection of the vector onto the vector .

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Q: Show that the column vectors (1,1,2,4),(2,-1,-5.2) (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Find a vector orthogonal to both ⟨1,−10,0⟩ and to ⟨0,7,4⟩ of the form

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Q: Determine the vector projection of the vector (5,0, 7) on the vector (–1,3,4).

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