(12 4 A= 2 13 23 4 23 77 2 b= 4 2 b) a) Show that the matrix A is positive definite. Find the Cholesky factorization A=GG¹. c) Solve the linear system Ax=b.

Q: 8. Find a, b and c such that the matrix a V2 V2 A = |b

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Q: Q2) Use Cramer's Rule to solve the following system : y = 2 – 2x + z x - y = 7- z 2x + 2y = 4- z

A: Rewrite the equation as follows 2x+y-z=2x-y+z=72x+2y+z=4   write the equation in matrix form…

Q: Q1) solve the system Ax=b by using LU factorization. A= [8 8 6 3] [3 1 7 1] [7 6 7 4] [9 6 1 8]…

A: We solve given system by LU decomposition.

Q: Adopt Cramer's method to solve any consistant system of linear equations having three variables x,y,…

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Q: Find the (1, 2) cofactor of the matrix A = b) 2 d) -18 f) -9 e) 18 9 3 4 -1 2 -1 2 3 -3 -3

A: given A=32-1423-1-3-3 cofactor of Element (1,2)=-11+2M12=-M12 where Mij=minor of (1,2)

Q: 4) Consider the system of linear equations: X1 + 5x2 + 3x3 = 4 X1- X2 + 6x3 = 16 2x1 + X2 =D5 a)…

A: Given the system of linear equation is  x1+5x2+3x3=4 x1-x2+6x3=16 2x1+x2=5 a We write the given…

Q: 2x+5y =9 x+2y-z=3 -3x-4y+7z=1 a) Setup the augmented matrix. b) Solve the system by Gauss-Jordan…

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Q: Let A = 2 [33] 34 a b -[:] d a) Find all matrices B AB = BA. b) Use the results of part (a) to…

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Q: Inverse Matrix Method.

A: Given equations are x + 2y + z = 2                        ... (1)2x - y - z = 1…

Q: 4) Consider the system of linear equations: X1+5x2 + 3x3 = 4 X1-X2+6x3 = 16 2x1 + x2 %3D %3D = 5 a)…

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Q: 4) Consider the system of linear equations: x1 + 5x2 + 3x3 = 4 х, — х2 + 6х; %3D 16 2x1 + x2 = 5 a)…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: 4 1. 1FA-(165) and B-(²- If A= -2 6 8 - 10

A: Given,             A=45-69 and B=-268-10. We have to find 1) A+B   and  2) 2A+3B

Q: Give a 4 x 4 elementary matrix E which will carry out the row operation R₂-4R3 R₂. E = Test that E…

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Q: 5 a 1 28 6 2 Find all a and 3 > 0 so that the matrix B = is 2 a diagonally dominant;

A: Consider a square matrix . Then the matrix is said to be diagonally dominant if it satisfies the…

Q: 4) Consider the system of linear equations: X1+5x2 + 3x3 = 4 X1-X2+ 6x3 = 16 2x1 + x2 %3D = 5 a)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the solution of the linear system using the Cramer rule 7x1 – 2x2 – 3x3 = -3 X1 + 5x2 + x3 = 14…

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Q: Hi, please see  the image attached and answer the questions that follow. also please use working and…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use Cramer’s rule, whenever applicable, to solve the system.

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Q: Find the matrix of the quadratic form. 13) 3x²+2x2+6×3 - 8x1x2 + x2x3 14) 10x1x2 - 6x1x3 + 14x2x3…

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Q: 5. Find the cofactor matrix and then solve the following system: 3x1 - x2 + x3 = 4 -x, + 7x, – 2x3 =…

A: We can write the above equation in following matrix form : 3-11-17-226-1x1x2x3=415   ::  AX=B. Co…

Q: nsider the system of linear equations: X1+5x2+3x3 = 4 X1-X2+ 6x3 = 16 2x1 +x2 %3D Write the system…

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Q: 2) Consider the following system of linear equations: Cz = w, where the coefficient matrix C and the…

A: a) The given system of equation is 2-iz1+i-4z2=1+2iz1+2iz2=3+i In real the system can be written as…

Q: x-2 1. A= 3x-6 4x-11 Given that the matrix A is singular, find the possible values of x.

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Q: 1. Consider the following linear system and use CRAMER Rule to solve the system: (0.3x₁ +0.52x2 + x3…

A: Given: Linear system-0.3 x1+0.52 x2+x3=-0.010.5 x1+x2+1.9 x3=0.670.1 x1+0.3 x2+0.5 x3=-0.44To find:…