21 AATC has vertices at A(-8, -5), T(8, -5), and C(4, 1). Determine the coordinates of the centroid. C(4, 1) A(-8, -5) T(8. -5)

Q: [] -3 -3 Let y = -9 uj -5 u2 5 Find the distance from y to the plane in R3 spanned by ul and u2.

A: Consider the provided question,

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Q: a u, (00) = Utt , и (0, t) — 0, и (т, t) — 0, (t>0) и (х, 0) %3D0, (0<x<n, и, (х, 0) %3 * (т—г),…

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Q: Q3. Consider the homogeneous CLTI system i = Ax where 01 -1 2 1 A -1 a) Is A diagonalizable? If not,…

A: Given that A=2100-12-101.  To check the matrix A is in diagonalizable form or not, first we will…

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A: This question can be solved using the concept of vector projection of a vector on other vector.

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Q: {(9,5,6), (3,5,6),(0,0,2), (4,6,0)} is linearly dependent in R'

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Q: Let T: R3 → R3 be a linear trans formation such that T(1,1,1)=(2,0,-1),T(0,-1,2) = (-3,2,-1) and…

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Q: 6. Prove that (i) the three points A(1,4,2), B(3, 2, 4) and C(5,0,6) are collinear, (ii) the four…

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Q: Let D4 = {1, a, a², a³, b, ab, a²b, a³b} and X = {1, a, a²,a³}. Find i. Centralizer ofX. ii. Center…

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Q: This is for Calc 4, told me to post under advanced math though, please help me solve

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Q: 1. Use Cramer's rule to find the value of x, in the linear system: X, +x, +x, = 5, -x, +3x, = 2,

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Q: {(9,5,6), (3,5,6), (0,0,2), (4,6,0)} is linearly dependent in R'

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Q: { (0,0,0), (3,5,6)} is linearly dependent in R ulgn O ihi O

A: Solve the following

Q: (d) Compute the cross product (0, 2, 1) × (1, 3, 1).

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A: Euclidean distance formula The Euclidean distance formula is given by             L2=x1-x22+y1-y22…

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Q: Froblem 1 f(z) = 1 + Z Determine its Laurent with center Zo: Z₂ = 0 لها

A: We find Laurent series in given cases.

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Q: 5. Use the matrix o Rotate polygom ABCD with coordinates A(0, 0), B(4, 1), C(S, -1), and D(-2,-3) -1…

A: Given A(0,0) B(4,1) C(5,-1) D(-2,-3)

Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

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A: Given :u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2)

Q: 2 2 A = 7. Give an LU-decomposition for A.

A: Solve the given problem.

Q: Q3. Consider the homogeneous CLTI system i = Ax where 2 1 A = -1 2 -1 a) Is A diagonalizable? If…

A: Given :-  Consider the homogeneous CLTI system x . = Ax where  A = 2100-12-101 To Determine :-  Is A…

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Q: ASSIG 5 EEE307 -1 2 31 4 5 Consider the system D=-3 4 5 6 i. Write down TWO Submatrices D1 and D2.…

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Q: Find the least squares approximating parabola for the given points. (1, 1), (2, -4), (3, 8), (4, 9)…

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Q: 88.aneqmtion for te plane passing through the Pts: ACl,2,3), B(2,3.1), C(3,1,2) 1s.. A)×-y+z=2…

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Q: (5b) Is E invertible? How do we know? (5c) Is E diagonalizable? How do we know?

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Q: 2. Thàngle LMN with vertices L(6, 6), M(8, 8), and N(8, 3): a) reflection in the linex = 5 b) 270°…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: 02)Determine Lohether the given yoetors are linearly defendant or .linearly independlent: -2 2. 2. 3…

A: The given vector,-213, 29-3, 23-3

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Q: 2 1 c is a serond dimension complex veetor U and v are elements of c² u= (34 ;, 24 2;), V= (2t;,-2…

A: To find- Euclidean  norm.

Q: In writing v as a linear combination of u ,u, &u, ( if possible) given: y = (3,0, – 6) , u , = (1, –…

A: The given vectors,v=3,0,-6, u1=1,-1,2, u2=2,4,-2, u3=1,2,-4

Q: Find the linearization L(x,y,z) of the f(x,y,z)= 8 square(x^3+y^3+z^3) at the point (1,2,3)

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A: Reflection Matrix about the xy-plane is : Rxy=10001000-1 Reflection Matrix about the xz-plane is :…

Q: 6. Prove that (i) the three points A(1, 4, 2), B(3,2,4) and C(5, 0,6) are collinear, (ii) the four…

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Q: A=30 ,B = Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C)…

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