Let T : P3 → R° be defined by Г2а — 26 — с +dT a – 36+ 2c – d. Let u = a° – 2, B = {1, æ, x², x³ }, and T (ar + bx² + cx + d) -3a + 36 + 2d C = 2 -2 -1 1 Given [T -1 -1 3 -2 , use the Fundamental Theorem of Matrix Representations to find 6 -2 Pc(T(u)). Ex: 5 Pc(T(u)) =

Q: Let A and B be square matrices of order 6 such that det(A) = 4 and det(B) = 15. Compute the…

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Q: Is the composition T1 o T2 also well defined? Why or why not? Use the definition of a composition…

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Q: -3.x1 Let T : R³ → R² be defined by T 3x2 + x3 6 Let B = { u1 = U2 = U3 = and C = { v1 = V2 = 4 What…

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Q: Let A and B be 6× 6 matrices with det(A) = -10 and det(B) = 5. Use properties of determinants to…

A: This question is related to matrix and determinants, We will solve it using given information.

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Q: A linear operator T: P2 P2 is defined as T(p(x)) = p(2x+1), i.e. T(c + c₁x + c₂x²) = C₁ + c₁ (2x +…

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Q: Let B be an invertible matrix in M (R). Define T: M (R) → M_ (R) by nxn T(A) = B AB. Prove that T is…

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Q: Let T : P3 → R' be defined by За — 2b + 2с+d | T (ax3 + bæ? + cx + d) а — с — 2d . Let u = r³ – 2, B…

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Q: 2. Let V = Mn(R). Show that the symmetric bilinear form : V xV →R given by (X,Y) = tr(XY) is…

A: The complete solutions are given below

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Q: Suppose a certain translation T sends P(xp, yp) to Q(xo,yo). Find the 3 x 3 matrix T that represents…

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Q: Let A e C™×n; that is, A corresponds to a linear operator C" → C*. Define the Hermitian transpose A*…

A: Given: A∈Cn×nA*=Hermitian transpose of A.Ax·y =x·A*y     ∀x,y∈CnTo prove:A*ij =aij

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A: The Polynomial is the characteristics polynomial for given matrix.

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Q: šhów thát, for n>U_multiplication of multipličátión óf nxn rotation matrices is generally not…

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Q: Suppose T : R4 → R' is defined as: T(x, у, z, w) %3D (х + у + z, х — z, у + z+ w). - Find bases of…

A: The given linear transformation is T:ℝ4→ℝ3 is defined as:           Tx,y,z,w=x+y+z,x-z,y+z+w And the…

Q: 2. Let A E Mn (R) be a skew-symmetric matrix, i.e. AT A. Prove that (a) x" Ax = 0 for all r E R".…

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Q: Let T : R² -> R² be defined by T ( 3x1 – 12 -1 B = 2 , and | . Let u = %3D -3x1 + x2. {{}} C = Given…

A: Consider the given information.

Q: Consider the mapping D: M, → R, defined - where A is a 2x2 matrix – D(A) = |A| (determinant). Show…

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Q: Let T: R3 - R2, definity by T (x, y, z) = (x + 2y-z, x + 3y) where B1 and B2 are the canonical bases…

A: We have…

Q: Suppose A E M,xn(C) is a normal, invertible matrix. Prove that A A- is unitary.

A: Given A € Mnxn(C) is a normal matrix.

Q: 1. Let A = [a;j]4x5, B = [bij]4x5; C = [cij]5x2; D = [d:j]4x2, and E which of the following matrix…

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Q: Let A and B be n X n orthogonal matrices. (a) Prove that A{AT + BT)B = A + B. (b) Use part (a) to…

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Q: Let f(x, y, z) = x°yz + 3z – 6xy + 2. - a) Compute the Jacobi matrix of f b) Compute the Hesse…

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Q: Consider the functions f(x, y, z) = xyz and g(t) = (cos(27t), sin(27t), e*) 6. (a) Compute Df(1,0,…

A: f(x,y,z)=xyz(a) Df=i^∂f∂x+j^∂f∂y+k^∂f∂z   =i^∂∂x(xyz)+j^∂∂y(xyz)+k^∂∂z(xyz)…

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Q: -(:)- Let T : R? → R² be defined by T -2x1 + *2 2 B = Let u = -2x1 – 3x2 and C = 1 Given Pc ,use the…

A: Given T:R2→R2 defined by Tx1x2=−2x1+x2−2x1−3x2. Let u=2−4, B=31,21 and C=32,11 Given PC=1−1−23. We…

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A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Let Y-Nn(0,E)and let A be any nxn symmetric matrix. Show that m.g.f of Q=Y'AY is M(t) : det…

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Q: Let B = uj = ,U2 = and C = , V2 = Find Pc, the transition matrix %3D from the standard basis of R2…

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Q: Let A and B be 4x4 matrices such that det(A) = 5 and det(B) = 3. Compute the determinant of…

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Q: Find the value of k for the linear operator T: R°→R°, such that T(x,y,z) = (2x + ky,y, (k-2)y +z),…

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Q: Given two Hermitian matrices X and Y , where XY not equal to Y X, prove XY −Y X is not a Hermitian.

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Q: Cônsider the BVP u =n?cos(nt),0<t<1, u(0) = 1, u(1) = -1. %3D Using the central difference quotients…

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Q: 3. Let A and B be square matrices of order 3 such that det(A) = 10 and det(B) = 12. Compute the…

A: From the given problem;   detA=10 ; detB=12   a).   As we know that:   detAB=detAdetB   So,…

Q: Let T : P3 → R° be defined by а — 26 — с Т (ах3 + bx? + сх + d) а — 26 — с . Let u = x³ – 3æ, B =…

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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.