f = -x² - y² + 2xy. Diagonalize the quadratic form, i.e., find an orthogonal matrix P such that the quadratic form is diagonal with the change of variables Notation hint: you can enter numbers such as "1 / sqrt(2)". P: Consider the quadratic form = f = u² + 02. = P u V

Q: Find the matrix of the quadratic form. Assume x is in R°. 5x - 4x3 + 3x3 + 18x,x2 - 4x,×3 b. 3x -…

A: We want to find matrix of given quadratic form.

Q: Use row operations to change the matrix to reduced form. 1 1 1 17 2 3 8 27

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Q: Find the matrix of the quadratic form. Assume x is in R?. a. 3x - 8x,x2 + 2x3 b. 5x, + 18x,x2

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Q: Calculate the 3x3 determinant: 3 2 -5 -3 4 -3 -6-7 -4

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Q: Let A = {ª₁,2,ª3} and B = a₁ =3b₁ b₂, a₂ = − b₁ + 5b₂ + b3, a3 = b₂ − 2b3. a. Find the…

A: a. Find the change-of-coordinates matrix from A to B.b. Find [x]b for x = 2a₁ +3a2+ a3.

Q: Use row operations to change the matrix to reduced form. 1 1 1 19 569 31

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Q: 1. Solve with matrices: -7x₁ +5x2 - 6x3 = 3 5x12x2 + 3x3 = 5 X1 X2 + x3 = -2

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Q: Determine whether b is in the column space of A. A = 1. -102 5 8-10, b = -3-3 6 3

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Q: Given that −1=−4x−3y and −5=7x+6y, find the values of x and y using the inverse of a matrix. Give…

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Q: Given the matrix: A= [1 -2 1 3]. Perform the operation

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Q: Use row operations to change the matrix to reduced form. 1 1 1 18 5 6 7 24 1 1 1 18 5 6 7 24

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Q: 15 Use Use the Inverse matrix (x-4y=D5 4x -15 y= 20 %3D

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Q: Consider the three equations: x - 2y = -1,3x4z = -1 and 2x +2y+z=2. Write these in the form of Ax =…

A: Given equations x - 2y = -1 3x - 4z = -12x + 2y + z = 2

Q: Find the matrix of the quadratic form. Assume x is in R². a. 9x² - 16x₁x2 +6x2 b. 4x² + 12x₁x2 2 a.…

A: We have to find the matrix of the quadratic form. Assume that x is in R2.Matrix of the quadratic…