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: -2 -1 2 y 55 15 1 3.

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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: Find the matrix of the quadratic form. Assume x is in R³. a. 2x² +8x² − 3x²3 - 10x₁ x₂ + 8x₁×3 −…

A: Concept

Q: Express the quadratic form (c₁x₁ + C₂X₂ + ... + Сnn)² in the matrix notation TA, where A is…

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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: Ql: By using matrix inverse method. Find the value of x and y in term of z. 2X + Y-Z 3 X-3Y+2Z-1

A: Let us determine the values of X and Y in terms of Z using matrix inverse method in the next steps.

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

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Q: Зх — Зу — 6z %3D -3 2х — 2у — 4z 3D 10 2х + Зу + z % 7

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Q: ? 3x1 – 2x3 4x1 х — Xә + хз X1 ? ? ? X2 ? ? ? X3 ||

A: We have to fill the missing entries of the matrix, assuming that the equation holds for all values…

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

A: This is a problem related to matrix. We will find out square of the matrix and then calculate f(A)…

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: TRUE OR FALSE In each case, explain or prove your answer. If U is the reduced row echelon form of A,…

A: We have to check whether the given statement, " If U is the reduced row echelon form of A, then A…

Q: Checking relation properties by using matrices.

A: To check the properties of relation using matrices.

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: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A: According to the given information, it is required to find a linear dependence between the columns…

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

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Q: Solve using matrices. 7x+6y = 32, 13. -x+8y = 22

A: We can solve the given equation by using augmented matrix.

Q: Write down the quadratic form for the matrix: 1 1 2 A = 1 1 0 2 0 4/

A: The quadratic form of matrix a11a12...a1na21a22...a2n............an1an2...ann…

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: Suppose A is an invertible symmetric matrix. Then the inverse of A is also symmetric. (A) True B)…

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Q: Give the matrix representing the relation in the previous problem. Label the rows and columns.

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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…