Question 1. Determine the LU decomposition with pivoting by hand. 3x1 - 2x2  +x3  = -10 2x1 + 6x2  -4x3 = 44 -x1 - 2x2 + 5x3 = -26

Q: Find the Jacobian of the transformation x = 5u + 6v, y = u² + 7v

A: Let us consider the function x=x(u,v) , y=y(u,v) The Jacobian of the function is obtained as…

Q: Decomposition fields are algebraic extensions.

A: Definitions:Decomposition fields(splitting field) :  A splitting field of a polynomial p(X) over a…

Q: Find Tay br Polynomial. for the function fox): Vx + 3. ot degree 3 centered ata=2

A: According to the problem, we have

Q: Express the polynomial a+ 3 +a2 + 2r as a product of its irreducible factors in Z,lr).

A:

Q: 8z Compute the inverse z-transforms of z²-6z+25

A:

Q: QI: using the Bairstow's method to find a complex root for f(x) = 50 – 8x - 62x + x*, where (x2) is…

A:

Q: Show that the transformation Y = 2x, + x, + Xy, y2=x, + Xg + 2x, yg-x, - 2r, is regular. Write down…

A:

Q: A PSR is the congruent image of A PQR after a transformation. P R True False

A: Given: The statement, "△PSR is the congruent image of △PQR after a transformation" in figure , To…

Q: what are the transformations of y=6/x-2  -3

A: Y= aF(x-h)+K  Here h and k represents horizontal and vertical shifts according to their signs  a…

Q: Question 1 Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable…

A: 1.1 First of all  we need to make a change of variable substitution x=Py that transforms the…

Q: Find an LU decomposition of 7-779 A= -1 -1 11 7 1-3 -1 21 -1 17 15

A:

Q: Yi 6x1 -1x2 Y2 —17х1 +3x2 I|||

A: Given linear transformation T is  y1=6x1-1x2y2=-17x1+3x2 Its inverses is the function T-1 from y to…

Q: Find a singular value decomposition (SVD) for A = Verify that A = UEVT.

A:

Q: A triangle is defined by the coordinates P1(3, 0, 0), P2(0, 5, 0) and P3(0, 0, 7). The triangle is…

A: NOTE:- By Bartleby rules, only part (a) is done A triangle is defined by the coordinates…

Q: 4. Find the Lagrange and Newton interpolate polynomials P3(x) of nodes (-1,3,5), (1,-5.5), (2,-1),…

A:

Q: 1. Consider the following data points (0,3), (1,0), (2, 1), (3,0) (a) Derive the monomial…

A: Given data point is (0, 3), (1, 0), (2, 1), (3, 0) Solution a: For 4 data point, monomial basis,…

Q: Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In|4x +31)], transform it to z. A.…

A:

Q: Let A = LU be the LU decomposition of A. Then R(A) = R(U). True False

A:

Q: Why does every linear transformation T from R 2 to R 2 take squares to parallelograms? Rectangles…

A: We have to explain whether every linear transformation T : ℝ2 → ℝ2 take squares to parallelograms,…

Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

A:

Q: a) Find a Lagrange interpolating polynomial in the form of P, (x) = ax³ + bx² + cx+d befitting the…

A:

Q: Find the roots of the following equations, assigning the results to ra, rb, and rc respectively a)…

A:

Q: (a) (b) W₁ = 4x1 + 5x2 W₂ = x1 - 8x2 W₁ = 5x1 - 7x2 W2 = = 6x1 + x2 W3 = 2x1 + 3x2

A: Given that (a)             w1 =4x1 + 5x2            w2 = x1 − 8x2   (b)            w1 = 5x1 − 7x2…

Q: Question 2: For which real values of a do the polynomials P1(t) = at? -t-; P2(t) = - + at -; P3(t) =…

A:

Q: 1 a b a,b,c e R including A = 0 10 0 0 100 Let the matrix be given. According to this,

A:

Q: Write down the 2 × 2 matrices that represent the following linear transformations ofthe plane. Also…

A: As per guidelines, we will solve first three subparts of the question only. a) We have to find the…

Q: 10 - Which one is the highest order Lagrange polynomial of the grids below? Xị Yi -2 3 1 -1 x2—9х-8…

A: We have to solve given problem:

Q: Let plx) be the Lagrange interpolating polynomial that C-2,3), (2,4), (4,3) Aits the data the n P(3)…

A: See the attachment

Q: Xị – 5x2 – 4x3 3x2 + 4x3 • X1 - for all a E R³. X2 T(7) %3D %3| -2x1 + 6x2 X3

A:

Q: 2. Let k be a complex number and P(x) = 8x³ − 4kx² + (2k+6)x +3. Find all values of k for which P(x)…

A: Given the polynomial  P(x)=8x3−4kx2+(2k+6)x+3 , we need to determine the value(s) of  k  such that…

Q: Draw a transformation diagram for v = (3/5)c, with the numbers 1, 2, and 3 (in meters) on the…

A:

Q: 105 find a matrin A = singulay decomposition of

A: The objective is to find singular decomposition of the matrix A=110110 Now, AT=101110 Let,…

Q: Show that the Newton divided-difference polynomials 3 – 2(x + 1) + 0(x + 1)x + (x + 1)x(x – 1) and…

A: Given: Let P(x)=3-2x+1+0x+1x+x+1xx-1    Q(x)=-1+4x+2-3x+2x+1+x+2x+1x

Q: 2. (a) Define the dot product of two polynomials p(x) = ao+a₁x+a₂x²+a3x³ and q(x) = bo+b₁x+b₂x²+b3x³…

A:

Q: A straight line defined by its end points (6, 3) and (13, 6) is to be scaled by a factor of 2 and…

A: First of all we will determine the equation of the line by its end points (6,3) and (13,6). Slope of…

Q: (1) (2) If r is an independent variable and with a subscript (like a,,,, etc.) represents given data…

A: