Let uj = (1,1,2), uz = (1,3, –2), uz = (4, –2, –1) in R’. Show that uj , uz, Uz are orthogonal, and write v as a linear combination of u1, u2, Uz, where (a) v= (5,-5,9), (b) v = (1, –3, 3), (c) v = (1,1, 1). (Hint: Use Fourier coefficients.)

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

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Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

A:

Q: Let u, v ,w be three linearly independent vectors in a vector space. Determine a value of k, so that…

A: Given Let u, v ,w be three linearly independent vectors in a vector space Now we have to find value…

Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

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Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: we have to find the vector in linear combination form

Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

A:

Q: 1.2.4 Prove that vectors (1, 1, 1)", (2, 1,0)", (3, 1, 4)", and (1, 2, –2)" are linearly dependent.…

A: Let v1, v2, v3 and v4 are given vectors that is v1=111  ,  v2=210 , v3=314 and v4=12-2 Claim:    v1…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: S=1,2,3,4,1,0,1,2,1,4,5,6 Here use definition of linear dependent set  Let V be a vector  space over…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A:

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

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

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Q: Let u=(-1,37 and u =< 2,-57 Find the Component form of the vector Su-V

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Q: Assume that 0 < a <1 and 0 < b <1.Find the stable vector of 1- a a P = b 1-b w = [ ]

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Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

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Q: Find u × v and show that it is orthogonal to both u and v.u = (−2, 1, 1), v = (4, 2, 0)

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Q: Prove that if {Vi, V2, v3} is linearly independent, then so too is the set {u, u2, u3 where u = V -…

A: Introduction: Linear dependence and linear independence of a given number of vectors are very…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: See solution below

Q: Let u1,...Ūk E V be linearly dependent vectors, and k > 2. Prove that there exists j, 1 < j < k,…

A: Given- Let v1→, ……, vk→ ∈ V be linearly dependent vectors, and k ≥ 2.  To Prove- Prove that there…

Q: Two vectors in R2 are linearly dependent if and only if they lie on a line through (0,0). Select…

A: We have to check it is true or false  Two vectors in R2 are linearly dependent if and only if they…

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

A:

Q: Find u × v and show that it is orthogonal to both u and v.u = (1, 1, 0), v = (0, 3, 0)

A: We have given; u = (1, 1, 0), v = (0, 3, 0)

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A:

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

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

Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

A:

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=&lt;-1,0,1&gt; v=&lt;3,2,1&gt; w=&lt;0,1,2&gt;

Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Here, u=(1,2,3,4),v=(02,t,3) &amp; w=(1,1,0,1)

Q: Let u = (1,2, –1,5), v = (0, 1, 1,0,) and w = (3, 4, –2, 15). Show that u , v and w are linearly…

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Q: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

A: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

Q: Suppose T: R³ → R² is a linear map and that u and v are particular vectors in R. If T(u) = (2, –3)…

A: Given query is to find the indicated vector.

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: We solve this in step 2

Q: Prove that if (V1,V2, V3} is linearly independent, then so too is the set (u,u2, u3} where u, vı-…

A:

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: the set is linearly dependent if α1,2,3,4+β1,0,1,2+γ2,6,8,10=0,0,0,0  at least one of α,β,γ is non…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: Given : s = {(1,2,3,4), (1,0,1,2), (3,8,11,14)}

Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

A:

Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

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Q: Consider the sets of vectors  S={u,v,w} and T={u,v,w,x}. Which of the following is true:  -If T is…

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Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A:

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of 1 - a а P = 1 - b [ W =

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Q: Let S = { t² + 1, t² – 1, t – 2}. - 2. If S is linearly independent in P2, write 2t2 – t + 5 as a…

A: Three vectors A,B,C are said to be linear dependent, then there exist three numbers a,b,c such that…

Q: Let S = {v1,v2, V3} be a linearly independent set of vectors in {u1, U2, U3}, where u̟ = vị + v2 +…

A:

Q: Find u × v and show that it is orthogonal to both u and v.u = (12, −3, 1), v = (−2, 5, 1)

A: Given vectors u=12,-3,1v=-2,5,1 Their cross product is u×v=ijk12-31-251…

Q: Let u, v, w be three linearly independent vectors in a vector space. Determine a value of k, k . so…

A: Given that: u, v, w are three linearly independent vectors in vector space and S={u-5v,v-8w,w-ku}

Q: The vector 1 is in Span{ V2, ., Vm } if and only if ( V1..., Vm ) are linearly dependent. O True…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: let a1,2,3,4+b1,0,1,2+c2,6,8,10=0,0,0,0 a,2a,3a,4a+b,0,b,2a+2c,6c,8c,10c=0,0,0,0 simplify…

Q: S. The image of the vector i + j – 2k under a mapping (1 2 3 defined by the matrix M, where M = 0 1…

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.