tind baves for the faw fundoarental Sues of thie matrix A as follows. NCA) = nullspore y a R(A) = colnan Spare of A Thin shaw that NEa) = R(A)t and MCA) = RCA)". 2 -3 3 NA) = NCAT). E}

Q: J PCAJ- 02 PC(B) = 0.6 nd PCA UB J-0,7, find PCAJ- 0.2 ,PCB) = 0.6 ,ond PCA UB)J=0,7,find and PCA…

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Q: If a vector (a) If AB, find a and B. (b) If ALB, find a and B. Ã=3ā¸+6ā„+ā₂and B = αã¸−2ケ ßā¸‚

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Q: Felse Deseribe all calutions of Aa. Vector form where the metrik belaw. You may vse Y and/01t as…

A: Every homogeneous system has at least one one solution. There are two equations and three unknown.…

Q: Is A = (2 ) diagomlizable? 4

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Q: 3. Give an example of an orthonormal set with 4 non-trivial vectors in R5.

A: We have to solve given problem:

Q: ,,,

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Q: Suppose that you have the following model and data to estimate the following equation Nobs Y X2 X3 1…

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Q: 19. Which of the vectors (A)–(C) in Figure 22 is equivalent to v – w? (A) (B) (C) FIGURE 22

A: The vectors substraction: (v-w)

Q: A=LDU where D-) then the humber of special solubion s bo Ax =0 is equal a-1/b.e/c.2/d.camt be deubie…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1. Given a vector a=(3, - 2, 2), the magnitude of a is and the normalized vector of a is_

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Q: 8. Let 1 2 +--+- () -- () ---(3) (:). at = and = 3 4 7 b3 (a) Find conditions on b₁,b2, b3 such that…

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Q: Let (3) 1 V = (b) Cosine of the angle between v onto w is also called the correlation between them…

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Q: 8. Consider the vectors [11, 2, 0, 1, 0, 2], [0, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 1]); [0, 1, 1, 1,…

A: Remark: If no column (row) of a matrix can be written as linear combination of other columns (rows)…

Q: 4) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.5., # 24, or from your…

A: see below the answer and explanation

Q: elations R = {(1,2), (2, 3), (3, 1)} and S = {(2, 1), (3, 2), (1,3)} on the set A = {1, 2, 3}. d)…

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Q: 5. Consider a vector va Could we write this equivalently as va

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Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: 14. Find a vector perpendicular to both of the vectors * (ũ + v) and (ũ – v) where ủ = 2i – j + k,…

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Q: 8. Which of the following are orthonormal s 1 A = {U₁ = (₂0₁2), U₂=(2,0, B = { U₁ = (2,0, ₂2), U₂ =…

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Q: 2- For asymmetric matrix 3x3 matrix dij =0 if, a) i+j=0; b) i-j=0; c) i-j=1. 3-For a symmetric nxn…

A: Symmetric Matrix

Q: a) Given the following matrices a = -and c= nd 2. 3 and C = 2. i) AT C. i) 2(BC"). i) D if (2AB)" =…

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Q: CMaxs, -) is Q3/Prove lat the Identity element in J. the matrix Au an ai3 eIR I. 923 Lazi a32 a33…

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Q: Obtain a set of orthonormal vectors by Schmidt method: u = (1, 1,0,1), uz = (2,0,0, 1), uz (0, 2,3,…

A: According to gram Schmidt method  orthogonal vectors can be obtained as: x1=u1x2=u2-<u2,…

Q: Only B and D

A: We will find out the required solution.

Q: Hefined or of length e colculated using Olnlan) operations n=2 then the

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Q: Normalize the vectors a ---4:0

A: Here we have to normalize the vectors a and u.

Q: Yi = Bot Biti tôi i=1,2,....n where ~ N(0, ²) as a general linear model (e) The hat matrix is…

A: Given that:A linear model isThe general linear model is To show:(e)  is symmetric and idempotent.(f)…

Q: 2. A = flnd det 'A), adj CA) and inverse mateix

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Q: 21. Determine if each vector equation represents the same line as l1 : [x, y] = [-3, 5] + {[1, –4].…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.