Show that the condition number of the square matrix, X (generated with X;j = 461-2), grows i+6j–2 as a power law where n is length of one dimension of the matrix. What does this mean for

Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as…

A: It is given that, if a polynomial p(x) can be factored as a product of two lower degree polynomials…

Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

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Q: Show that the matrix X -1 : -1 -1 X : 0 : : X is Positive Definite if x > √n −1 The lower right…

A: The given matrix is An=x-1...-1-1x00::⋱:-100x. To Prove: This matrix is positive definite if…

Q: f is represented by the matrix: A = (0 2) (7 8) Show that f is invertible and find the…

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Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

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Q: Invert the following matrix 3x – 2y = 9 -x + 3y = 3

A: Solution: Consider the given system of equations: 3x - 2y = 9-x + 3y = 3 The coefficient matrix of…

Q: 32. Suppose the characteristic polynomial of a 3x3 matrix has 1 root at zero. What is the nullity of…

A: Eigen values and Eigen vectors: Let A be n×n matrix. λ is said to be an Eigen value of the matrix A,…

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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Q: 3-18. Show that the matrix 2 1 1 1 3 2 13 is a root of the polynomial p(x) = x& – 5x² – 5; that is,…

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Q: Find the matrix exponential of -3x1 + 8x2 x2 = 12x1 – 7x2 and use the matrix exponential to solve…

A: Given that  x1'=-3x1+8x2x2'=12x1-7x2 and the initial conditions are x10=1,x20=-1 The objective is to…

Q: Consider the following 3*3 matrix A=100,1-2-2,141 Show with your calculations that the matrix is…

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Q: 8 Consider a square matrix B whose inverse is given by B'. a In terms of B", what is the inverse of…

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Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / alpha, where alpha is…

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Q: 13. Find an estimate for det (A) if A is an n × n matrix whose entries form some pattern of +10's

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Q: Determine a QR factorization for the matrix given below: Note that you can type in square roots as…

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Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: Ak = PDP-1 (a) Show by mathematical induction that for a n x n diagonal matrix D with diagonal…

A: Let us prove the given result by induction or by taking induction on order of diagonal matrices.

Q: i. Let A, B; 3x3 order square matrixes, Meets the conditions BA=A3 & A3 – 2AB = 1 Prove that A is…

A: Given that A, B; 3×3 order square matrixes, meets the conditions BA=A3 & A3-2AB=I.…

Q: True or false: If A, B are square matrices of the same size, then A² − B² = (A + B)(A − B).

A: The statement you mentioned is incorrect. The correct expansion of the expression A^2 - B^2 is as…

Q: Consider the quadratic form: =2x₁²-6x1x2+8x22 a. Find a matrix A such that q(x)=x Ax. You do not…

A: Step 1:Step 2:Step 3:Step 4:

Q: Use matrix multiplication to find the dilation of (a, b) with factor k = α, where α > 1

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Q: 5. Let A be a (3×3)-matrix with the characteristic polynomial pA(x) = (2 – x)(x² + 1– a²) for some a…

A: Solution (a):- Given Characteristic polynomial of matrix A =  (2-x)(x2+1-a2) But we have to find the…

Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

A: Given :                    2-134-32321 To find :                 The cofactors for C13 , C22 , C32…

Q: For the matrixA=daig(-2,-1,2), put the following values in increasing order: det(A), rank(A),…

A: The given matrix is,  A = diag(-2, -1, 2). We have to put the following quantities in increasing…

Q: Suppose A is a 2 × 2 matrix, where -2 | u = Au = -4 A?u = 4 A³u 2 20 – 20 – 10. The minimal…

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Q: Discovery 4.6. Consider 1 -3 -1 A = 1 3 %3D -2 2 3 -1 -2. Compute the product AX by considering X as…

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