Make a change of variable, x = Py, that transforms the quadratic form 6x +18x1x2 + 6x2 into a quadratic form with no cross-product term. Give P and the new quadratic form. Which of the following matrices can be used as P in x = Py to produce a quadratic form with no cross product term? OA. √2 √2 √2 √2 OB. √√2 √√2 ... √2 O c. √2 √√2 √√2 O D. √2 √2 √2 √2

Q: a) Find the matrix of the quadratic form. Assume x is in R3 5x3-x3 +7x3-5x1x2 -3x1x3

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Q: Question 13 Which of the following products is an example of 'Difference of Squares'? a3 +1 2? + 6x…

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Q: Find the matrix of the quadratic form. 8x1x2-10x1x3 + 8x2x3 Select one: OA. 08-10] 80 8 0 O B. O C.…

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Q: Perform the given row operations: -6 -5 -4 - 6° 1) - 3 2 R2 + R1 7 - 4 4 7 -7 -6 3 5R3 → R3 -7] 2) 6…

A: To perform the given row operations.

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

A: Concept

Q: Give bases for row(A), col(A), and null(A). row(A) col(A) null(A) 2-4 201 2 1 2 1 1-2 3 2 2 000 0000

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Q: Find the matrix of the quadratic form 2x12 + 3x22 – x32 – 4x1x2 - 2 x1X3 + 6 x2x3 2 2 -1 2 -2 1 (a)…

A: We have to find Matrix of the given Quadratic form.

Q: ii. the missing elements of the adjoint of M, (-11 1 13 adj(M) = -9 an a2 3 a a33) :=

A: A detailed solution is given below

Q: Let a and b be real numbers satisfying a² - a -1 = 0 and 6² - 36 - 2 = 0, and let V = 1 a b ab (a)…

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Q: Give bases for row( A), col( A), and null(A)

A: The given matrix is A=110101-1101-1-1 We have to find the basis for row(A), col(A), and null(A).

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: Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

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Q: Perform the given row operations: 3 7 -8 -87 3-2 -7 R₁ R3 -7-8 5 1) 7

A: We have to perform the row operations as given instructions.

Q: Let A.3 be 5x5 matrices such that det (A) = 7 and det(A)=-3. Find the following (1) det(2(A^B)')…

A: if A is an n×n matrix and det(A)=a thendet(kA)=kn×adet(A-1)=1adet(AT)=adet(adj A)=an-1

Q: Express Ac as a linear combination of the columns of A.

A: Given A=2-34-1235-1-2   C=214

Q: Make a change of variable, x = Py, that transforms the quadratic form 3x, + 14x, x, + 3x, into a…

A: To find the solution of the given problem we find the matrix representation of the quadratic form.…

Q: Find the matrix of the quadratic form. 5x + 3x² + 2x3-8X1X2 + X2X3 Select one: O A. 5 -4 1/27 -4 30…

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Q: Give bases for row(A), co(A) row (A) K(A) -3 41

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Q: Solve the following set of simultaneous equations using the matrix inverse method: X₁ + x2 + 2x3 = 6…

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Q: Find the matrix of the quadratic form. Assume x is in R². 9x² - 12x₁x₂ + 8x²2 b. 8x² +10x₁x2

A: The quadratic form:a) b)  To Find:Matrix of quadratic form.