The objective of this problem is to write a polynomial p(x) = a + bx + cx2 in the form of p(x) = k1 +k2(1−x)+k3(1−2x)(1−3x). (a) Describe how would you construct a matrix for this purpose. Use E = {1, x, x2}. (b) Write p1(x) = 1 − 2x + 3x^2 in the desired form. (c) Write p2(x) = 3 + 2x − 5x2 in the desired form.

Q: 3. (a) Solve the matrix equation for X: -1 0 1 1 2 1 1 -3 1 -1 3 1 -1

A: If Ais a m×n matrix and B is a n×p, then AB is m×p Hence here X is 2×3 Let X = abcdef Thus…

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as…

A: It is given that, if a polynomial p(x) can be factored as a product of two lower degree polynomials…

Q: or each of the matrices below, find the associated quadratic form. -1 (a) 7] 4 b) (c) 1 -1 4] 14 4 1…

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Q: Section 2.2 1. Find the inverse of each matrix or determine the matrix is singular. 4 -3] (a) s [1 0…

A: As per our guidelines we will only answer the question number 1 .If you want more answers of the…

Q: Is the following statement correct or incorrect: The matrix notation of the quadratic form Q (xı,…

A: Solution : Given 2 variable quadratic form is                     Q(x1,x2)=5x12-10x1x2+x22 We have,…

Q: -1 -1 | | 4. For the semidefinite matrix A = -1 2 -1 write x' Ax as a -1 -1 sum of two squares.

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Q: plve for the unknown values using Decomposition Methods

A: We have to solve the linear system of equation using decomposition method.

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: 5. Solve the system of equations 3x, - 2x2 + 2.xs = 10 *1 + 2x2 – 3xs = = -1 4x1 + x2 + 2x3 = 3 (a)…

A:

Q: Let A = - 3 7 6-1 -3 -6 and B= 0-2 9-6 Solve the matrix equation - 3X + 4A = B for X. -4 -1 X =…

A: To find matrix X

Q: 1 3 3 - 4 1 A(x)=x² – A -2x+3 5 2

A:

Q: Which of the following is the solution for 剛 3] 长剧团-肉 = 0-2 - -5/2 3/2 №哟] -3/2] -5/2 3/2] 2-5/2…

A:

Q: For matrix A = (²3 §), if f(x) = X² - 2X, what is the answer to f(A)?

A:

Q: = 5.8. Let f₁(x) = x³ x² +1, f₂(x) = x³ + x² + x and f3 (x) = x³ + 2x²+3x+1 be three polynomials in…

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: An n x n matrix A (with real entries) is called a square root of the n xn matrix B (with real…

A: (a) find a square root of the given matrix B=1101. use definition of square root of a square matrix.…

Q: Consider the following function; Q(x1, x2, X3) = 2x? + 3x? – xž + 5x1x3 + x2x3 Find the matrix A…

A:

Q: 3 x 9 4 =39 solve for x matrix problem

A: Solving the problem by matrix multiplication formula.

Q: If the determinant of the 2x2 matrix 3 a 2 b is 7, then what is the determinant of the 2x2 matrix a…

A: To find the determinant of matrix.

Q: Given the polynomial P(x) = x* – 2x° + 2 – 3z + 7, find the remainder of division of P(x) by Q(x) =…

A:

Q: (a) Give an example of a 3 x 3 matrix A with C(A) = R³. (b) Give an example of a 3 × 3 matrix A with…

A:

Q: 3 1 Let A Solve the matrix equation -3 -1 XA - X = 2AT + I for X.

A: To solve the matrix equation XA-X=2A^T+I

Q: (c) Find the matrix corresponding to the quadratic form: Q(x) = 8x² + 7x2 - 3x² - 6x₁x₂ + 4x1x3 -…

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Q: (b) Solve for the matrix A if given 33(2A- 31)

A:

Q: -14 2k -81 9. Find the values of the variables 3f %3D 3 -3 3 10. Find the zeros of the polynomial r3…

A:

Q: For matrix A if g(X) = X² + 4x + 2, what is the answer to g(A)?

A:

Q: (ЗАТ + 4CТВ)Т- 54 - 4B

A:

Q: Given the matrix 2 1 A = |0 3 1 1 0 -1 and the polynomial p(x) = x³ + a.x² + bx + c, find the values…

A: GivenA=21003110-1p(x)=x3+ax2+bx+cp(A)=Op(A)=A3+aA2+bA+c=O21003110-1.21003110-1.21003110-1+a21003110-…