(a) find the matrix A of the quadratic form associated with the equation, (b) find an orthogonal matrix P such that PTAP is diagonal, (c) use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation, and (d) sketch the graph of each equation.9x2 − 24xy + 16y2 − 400x − 300y = 0

Q: 3 -3 -8 A = 3 -4 -12 1 -1 3.

A: Find the inverse of the matrix

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: Consider the fourth-degree polynomial equation a₁ + b₁x²q₁x² + b₂ a₂+ b₂x² a₂x² + b₂ a3 + b3x² a3x²…

A: Given that We know that determinant of a matrix is equal to zero if any two rows or two columns are…

Q: B = -2 {[1] ·[5]} and = {[] [4])} C 3 are bases for R². Complete the augmented matrix used to find…

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Q: a) Write the vector 2 as a linear combination of the vectors }]· 6 040 5

A:

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: 2y+3x+3z=18 x-4z=1 x-y+4z=9 -R+E+G=1 R-G+3E=18 5E+R-6G=7 Solve the above equations using the…

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Q: Express the following system of linear equations as a vector equation. 3 BHOHBHO x2+ 0 7 6 -6 3x₁7x2…

A: To express the following system of linear equations as a vector equation.…

Q: Find a vector that is orthogonal to each of the three vectors below: V1 = 1 V2 = 0 1 0 and V3 = 1 3…

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Q: Find the matrix A of the quadratic form associated with the equation.12x2 − 5xy − x + 2y − 20 = 0

A:

Q: Find the matrix A of the quadratic form associated with the equation.16x2 − 4xy + 20y2 − 72 = 0

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Q: Q.2) Use Inverse matrix method to solve the following equations: *- y +z = 1 2r – 2y + 2: = 2 -3r +…

A:

Q: (b) Find a real symmetric matrix C of the quadratic form: Q(x1, x2, x3) = x+ 4x3+ 6x3+ 2x1x2…

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Q: Find A-1 by forming [A| I] and then using row operations to obtain [I |B], where A-1 = [B]. Check…

A: Solution: Consider the given matrix is  A = 200040006 Let I denote the 3x3 identity matrix I =…

Q: 1 A = -1 2 For the matrix find A° using diagonalization.

A:

Q: Find the matrix A of the quadratic form associated with the equation. 9x² + 6xy - 8y² - 72 = 0 8.3 A…

A: Let us consider the quadratic form Ax2+Bxy+Cy2+D=0 then the matrix form is  AB2B2C

Q: x- 3y +2z = -6 4x-4y+5z -4 9x-5y + 2z = 2.

A:

Q: A = II 18x28xy + 18y² - 74 = 0

A: We can write any polynomial into quadratic form  if power is same eg: here x^2, Y^2, XY all have…

Q: Consider the following (complex, symmetric) matrix: B= 8 40 i 40 i -200 Determine the complex…

A: we will find the required.

Q: Q.2) Use Inverse matrix method to solve the following equations: x - y + 2 = 1 2.x – 2y – 2z = 2…

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Q: and (96) = C1 A₁-3+4i with ₁ = Write the solution to the linear system [+] in the following forms.…

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Q: (a) Find A-1. (b) Use answer from (a) to solve Ax = b. (c) Use answer from (b) to express b as a…

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Q: M = Find the determinant of the matrix -32x³ 8+2x² + 4x³ -x³ 1 + x² + 2x³ -2 +6x² 4 - 12x² 0 -2-3x²…

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

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Q: Using the matrices method (Kramer) solve the following linear equations *+2y+3z = -1 2x+5y+7: =-2…

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Q: For the matrix A=[a,j] = -9-10 -8 5 14 14 -8 13 15 MAX A (a) Find the minor of the element a23. (b)…

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Q: 3. a) Solve the following using Gauss elimination: x₁ + x₂ + x3 = 2 2x₁ + 3x₂ + 4x3 = 3 X₁ - 2x₂x3 =…

A: Answer is in below steps.

Q: Write the row vectors and the column vectors of the matrix. -3 1 [8 -2] 0 (a) the row vectors -3 0 1…

A: Given matrixThe horizontal elements in a matrix called elements of row vectorsThe vertical elements…