Let A be the matrix 5 3 2 Find p(A). p(x) = x³ – 2x + 4 p(A) =

Q: 1. Calculate exp(A) where A is the 2×2 matrix given by A 7 -2 -[33] = 5 5

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Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: Let A be the matrix Find p(A). p(x) = x – 2x +4 i 5 i p(A) = i

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Q: Find the matrix A if 3 1 4 A = 11 00

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Q: What is a, if A = 2 4 is a singular matrix ? a Simplify (1+x)(1+x²)(1 – x + x?) in descending order…

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Q: 5 -3 Find the matrix A if (I+ 2AT) ¯ = | 1: -2

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Q: -1 -1 | | 4. For the semidefinite matrix A = -1 2 -1 write x' Ax as a -1 -1 sum of two squares.

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Q: Find a matrix A that has an LU factorization where L is 4 x 4 and U is 4 x 3. L = U = 9. " 9-

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Q: Use the given definition to find f(A): If f(x) = a, + a,x + a,x2 + ... + a,x" is a polynomial…

A: We have to find f(A).

Q: Q1 (d): Find the rank of the matrix A. 1 0 5 0 1 -2 2 -2 -1 1 -6 3 -2 12 2 -3 0 2

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Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: Find the transpose of the resulting matrix: -100 A = 2 3 4 x 5 2 5-4

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Q: Consider the following function; Q(x1, x2, X3) = 2x? + 3x? – xž + 5x1x3 + x2x3 Find the matrix A…

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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: add new column [0;0;0] to the matrix a[12 3, 45 6 ,7 8 9]. * Your answer

A: We have to add column [0;0;0] to the matrix a[1 2 3;4 5 6;7 8 9]

Q: 3. Consider the matrix: 3 3 1 0 1 -2 Find p(A) where p(x) = x²- 1. Do not use a graphing calculator.…

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Q: [1-2 Q:Evaluate A-3A+91 where A = 2 3 3 -1 and lisa unit matrix. -3 1 2 3.

A: Given: A=1-2323-1-312 To evaluate A2-3A+9I. I is a unit matrix.

Q: 3 1 Let A Solve the matrix equation -3 -1 XA - X = 2AT + I for X.

A: To solve the matrix equation XA-X=2A^T+I

Q: Provide the symmetric matrix that generates the following quadratic form Q(x): x+2x+3x3 + x₁x2 - 2X1…

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Q: Given the matrix 2 1 A = |0 3 1 1 0 -1 and the polynomial p(x) = x³ + a.x² + bx + c, find the values…

A: GivenA=21003110-1p(x)=x3+ax2+bx+cp(A)=Op(A)=A3+aA2+bA+c=O21003110-1.21003110-1.21003110-1+a21003110-…

Q: Let A be the matrix 4 2 7 6 Find p(A). p(x) = x – 2x + 4 i i p(A) =

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Q: lue of x, if the g 5 10 is singula

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