Let B = {1+x, 1 – x², x + 2x²} and p(x) = 7+ 10x + 11x². You are given that B is a basis for IP2. %3D Ir [p(x)]g = then the value of B is

Q: Find the change-of-coordinates matrix from B to the standard basis in R². -5 1 •(3][4]} - PB B= -188…

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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: 2. Write the following in vector/matrix notation, specifying all components of the matrices. If it…

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Q: Find an invertible matrix P such that: 2 -2 1 P-1 -1 3 -1 P 100 2 -4 3. 0 0 6

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Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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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 A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: 2a. Write a MATLAB command that creates a row vector u that has the elements: Cos 3e 19π -2e, log10…

A: 2a. We write MATLAB command that creates a row vector u. Then we will find the maximum value of…

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: Find the change of basis matrix [B]. {0}{000) C = B = -2 -3 2 -2 -31 2 4 5 -3

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Q: Let C be a 6x6 matrix with. real eigenvalues -1, 2,4 and no complexores. Write the characterstic…

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Q: Write f= x + 10x1x2 + x3 as a difference of squares, and f= x? + 10x,x2 + 30x as a sum of squares.…

A: Given f=x12+10x1x2+x22.  Let the associated matrix of f be A=abba is 2×2 symmetric matrix. Then,…

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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

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