Suppose that A is a 10 x 10 diagonalizable matrix with eigenvalues 3, -2, and 1. Let c₁(x) be the characteristic polynomial of A. Fill in the blanks: €₁(x) = (x − 3)²(x + 2)³(x − 1)0 rank(31 - A) = rank(-21 - A) = rank(I - A) = rank(A) = Select a blank to input an answer

Q: Suppose that an n× n matrix A has a QR-decomposition where 1 -2 0 0 R = 0 1_1 0 -2 What is the…

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Q: . Let T₁ ([x2]) = [-2x₁ + 7x₂) + Find the matrix A such that T.(T.(X)) = AX ¹2 ([x2]) = [2x + ⁹*²].…

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Q: Consider the operator R2 → R2 given by left-multiplication by the matrix: A =[−2 −1,        1 −4].…

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Q: Let Q(x) = 7x} +x} +7x} – 8x1x2 – 4x1x3 – 8x2x3. Find a unit vector x in R3 at which Q(x) is…

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Q: Suppose that an nxn matrix A has a QR-decomposition where

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Q: Let A = [5 0 X = 5 Find an invertible matrix X and a diagonal matrix D such that X-¹AX = D. 001 D =…

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Q: Suppose A is a 2 x 2 matrix. Show that the constant term of the characteristic equation |A – XI| = 0…

A: According to the given data, shows that the constant term of characteristic equation is equal to…

Q: Suppose that the trace of a 2 x 2 matrix A is tr(A) = = 0, and the determinant is det(A) = -49. Find…

A: Given that the trace of a 2 * 2 matrix A is tr(A) = 0 and the determinant is det(A) = -49. Find the…

Q: A=(41] [4] ( )= (-1) [₂] + (3) [₂] 2

A: Matrix multiplication is possible if we have two matrices A and B such that, order of A =m×n;order…

Q: Let v1 = (1,−1,1),v2 = (2,1,3), and v3 = (−1,−1,2) be eigenvectors of the matrix A corresponding to…

A: We know that a number λ is called an eigenvalue of the matrix A if there is a non-zero vector x such…

Q: , a linear operator and a scalar λ are given. Show that is an eigenvalue of the operator and…

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Q: Suppose the matrix A is used to transform points in the plane iteratively. That is, given a point v,…

A: Given that A and B are similar matrices, and given that A=SBS-1 Now, λ is an eigen value of A and v…

Q: Find the characteristic polynomial of the matrix p(x) = de. = A 0 -2 -2 0 5 -3 -1 0

A: Given matrix is A = -5-2005-1-2-30

Q: Consider the function T : P2(R) → P2(R) given by T(a+ bx + cx²) = (a – b+ c) + bx + (-b+2c)x² Find…

A: Firstly we will find matrix associated with T.

Q: Let Q(x) = 143x² – 34x2 – 34x² – 36x1x2 – 36x1x3 — 72x2x3. Find a unit vector x in R3 whose first…

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Q: Let 4 = ²₁ 4 =1²2₂2₂] 2. a. Give the characteristic equation of A and verify that A satisfies the…

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Q: Let Q(x) = 35x²7x27x3 + 18x1x2 + 18x1x3 − 18x2x3. Find a unit vector x in R³ whose first entry is…

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Q: 2. Suppose A is a square matrix and A² = [0] (the zero matrix). (a) Explain why X = 0 is the only…

A: A is a square matrix and A2=0(the zero matrix)

Q: 2. Consider the quadratic form Q(r)=-6s²-10st-61². (i) Find the corresponding symmetric matrix. (ii)…

A: According to the guideline only three subpart can be answered. Please post other questions…

Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 7A +…

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Q: Fill in with the missing integers given that each of the matrices below is diagonalizable. (a) If A…

A: This question related to diagonalizable matrix .

Q: Consider the quadratic polynomial q(x) = 2x + 8x1x2 – 8x – 3x1 – 3x2 + 3. - - Find the symmetric…

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Q: Suppose A has 0 as an eigenvalue. What can you say about the determinant of A?

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Q: Find the characteristic polynomial of the matrix p(x) = || 5 -2 0 419 A = 0 -4 0

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Q: 3 0 0 -2 7 2. Find h in the matrix A= such that the eigenspace for A=7 is one- -1 0 4 -6 5 7…

A: Here, the matrix is A=3000-27000h-104-657 and the eigenvalue of the matrix is λ=7.