(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.xy − 2 = 0

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

A: Find the inverse of the matrix

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: 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: 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: Q3. Solve by Matrix Inversion Method the following set of equation: -1] [X1 1 X2 = 10 X3 -3 1 [2] 2…

A: We can write our question in the form of AX = B, and we need to find the X. For that find X = A-1B.

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: 2. (a) By transforming to matrix equation form, solve: 2.x- 3y = 11 7x+4y = 24

A:

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. 9x² - 6xy +9y² + 24z²31 = 0 A…

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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: 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: Do NOT row reduce! (a) Write the augmented matrix whose row reduction would find [x]B . (b) Write…

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

A: we will find the required.

Q: 7xi +4х2 -3x3 =2 + x2 +5x3 =-3 + 6х2 +7х3 --4 -2x+ 3х1

A: Given,

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

A:

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: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

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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: Consider the following quadratic form; F(x, y, z) = 5x? + 2y? + 4xy + xz

A: Symmetric matrix

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…