Find a vector g so that if F = (Co, C1, C2, cs) then F{f®g} = (co,0, 203, 0).

Q: show that the vectors: 2,3), II

A: To prove that the vectors:     v1=(1, 2, 3), v2=(-2, 1, 1), and v3=8, 6, 10 in ℝ3  are linear…

Q: find the domain of the vector-valued function.

A: Given: rt=1t+1i+t2j-3tk

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: 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: Find the length of the vector x=x= |x|=|x|=

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Q: Use the function to find the image of v and the preimage of w. T(Vy. V2) = ( V2, 2v1 - v2), v = (7,…

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Express vector t = (3, 6, -6, 9) as a linear combination of vectors u = (-1, 3, 0, 7) and v = (-5,…

A: The given vectors are: t=3, 6, -6, 9u=-1, 3, 0, 7v=-5,0, 6, 5 We have to express the vector t as a…

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

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Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

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

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Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Find the B-coordinate vector for p(t)=4+3t-2t²-5t³ B={1-2t²_t³,t +3t³,1 +2t+t²} a. (2,-1,2) b.…

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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: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: Find the B-coordinate vector for p(t) = -6+10t-7t² B={1-2t+t², 4-7t +5t², 5-8t+8t²} Enter your…

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Q: Let V1 = 2 V2 = 0 2 V3 = 2 V4 = 3 Decide the dependence or independence of the vectors {V₁, V2, V₁}…

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Q: Find u v. = (9, 2) v 3 (-8, 4) V: U V D

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Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: Let x and y be unit vectors. Find the value of (x-10y) (x+10y) (x - 10y) (x+10y) =

A: Given that 'x' and 'y' be the unit vectors. To find the value of

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

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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