Show that the CAPM Bi is linearly additive. Present all your calculations analytically and explain every step.

Q: • The Matrix B from 3 x 2 at by = 1- is 1. 3. 4. 1 -2

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Q: Show that matsix is not 15 diagonalizable A- 2 -3 2.

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Q: Calculate du u = x3 − x2

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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: Use the Gauss-Jordan method to find the inverse of the given matri single blank.) 1 1 0 1 0 1 0 1 1.

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Q: Determine: If S = {X2,1 + X2} is linearly independent or dependent.

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Q: Solve the following using Gaussian elminatic C, +2x2 -3x3+4sc4 =2 %3D SAR 53(,+12x2-7x3+ 6xcy =3

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Q: Evaluate. t*dt

A: Evaluating the definite integral

Q: Which of these statements best describes the trlangle?

A: Law of sine: - The rule of sines is the ratio of side length to the sine of the opposing angle in…

Q: Find the values of for which :=,0) and": =(a.1) are 4a-4 linearly independent in *".

A: To find the values of a for which the below vectors are linearly independent in R2. v1=4a−4, av2=a,…

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

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Q: Find an SVD of the indicated matrix.

A: The matrix is given of which SVD is to be calculated so,

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

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Q: If Ax = ax for nxn matrix A, nx1 matrix x, and a E R, determine a scalar 3 with the property that…

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Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: Calculate du:  u = x3 − x2

A: For a given function y=f(x) the differentials are dy,dx and are related as dy=f'(x)dx. This can be…

Q: Find diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

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Q: 3 If a + 1 is linearly dependent in R', find a. 2 a + 2

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Q: Let Xvuniform(0,8) then E(x-2)

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Q: The Matrix B from 3 x 2 at b = 1- - is %3D 1. 2. 3.

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Q: Suppose that the square matrix A is invertible. Show that the inverse of A is unique.

A: See below the explanation

Q: Suppose A is an m x mateix whose columns are linearly independent. What is the nullity of A?

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Q: Calculate the value of 1n(-V5 – V5i )

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: of the defir

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Q: Show that if, in using the Laplace development, you accidentally multiply the elements of one row by…

A: A 3×3 matrix a11a12a13a21a22a23a31a32a33.

Q: (c) 0 is neither diagonalizable nor

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Q: If A is diagonalizable, then A is similar to D. Select one: O True O False

A: Given   if matrix a is diagonalizable then A is SIMILAR  to D

Q: Show that A° = A°-0- and A-o = A- %3D

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Q: Solve the following linear system of equations using Cramer's Rule

A: We have to solve the following linear system of equations using Cramer's Rule.

Q: Please find all automorphisms. Thanks.

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Q: Which of the following DEs are first order linear DEs?

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Q: Solve the given SLE using LU-Factorization X + x2 + x3 = 3 X, - x2 + 4x, = 4 2x +3x, — 5х, %3D 0 |

A: Given SLEx+y+z=3x-y+4z=42x+3y-5z=0convertit in to matrix form1111-1423-5xyz=340convert it in to…

Q: write down in se quence steps in finding the the inverse OF matrix using the adjoint the matrix. OF

A: Let's find.

Q: Exercise 3.3.4. Verify that et and 1e2t are linearly independent. Hint: You must be a et and bit…

A: First take the three vectors:

Q: Suppose that Ax=b has no solution and the columns of A are linearly independent. Let t(A) denote the…

A: This is a problem of Linear Transformation.

Q: Use Theorem 1.4.5 to compute the inverse of the following matrix. [14 0 NOTE: Write the elements of…

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Q: Explain transpose AT of the m x n matrix A?

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Q: The linear Diophantine equation 11x + ny = 44 is solvable if, and only if,

A: We are given the linear Diophantine equation 11x+ny=44. For it to be solvable we must have gcd(11,…

Q: Suppose A=QR, where Q is m×n and R is n× n. Show that if the columns of A are linearly independent,…

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Q: S={(1,0,2),(1,1,1),(−1,15)} is linearly independent. True or false?

A: S=1, 0, 2, 1, 1, 1, -1, 1, 5 Now, 1 1-10 1  12 1  5=15-1-10-2-10-2=4+2+2=8≠0

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…

Q: Suppose a, = (1 -1 1 1) 5. a, = (1 0 1 0) %3D %3D az = (1 1 1 1)'a¸ = (3 2 3 0)" - Please find out…

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Q: Determine the standard matrix of a reflection in R² in the line 3x1 + 4x2 = 0. %3|

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Q: Determine the REF and RREF of the given matrix. pls show complete solutions

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Q: If A Is diagonalizable then Is diagonallzat Select one: O True O False

A: We will solve the following

Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…