Write the given system in the form x' = P(t)x + f(t). x' = 2x-5y+z+t y' = x - 9z+1² z' = 2y-9z++³ Χ y' = + 2-8- Z' y N

Suppose that you want to find the unique polynomial, y = f(x), of degree ≤ 6 that interpolates the 7 points (-2, 1), (-1, 3), (1, -4), (2, -6), (3, -1), (4, 3), (6, -2). (a) Write down the linear system that you need to solve to find the coefficients of this polynomial, and the augmented matrix of this system. (b) Solve the system from part (a) to find the coefficients of the polynomial (rounded to 3 decimal places) and write down the polynomial.

Write an equation for the line passes (through (8, 0) and (-1,3 (x/8) +(3y/56) = 1 O %3D 7x - 3y = 8 O 3x - 7y = - 24 O (x/8) + (7y/24) =1 O %3D y = -7x +56 7x + 3y +56 = 0 O 5x + 7y = 25 - x - 3y + 8 0 O

2 -dydx -I -VI-2 Vi-z²

X1+iy,=x2+iy2* *ュー,0 2

Find the values of x and y for which (x + y, 0) = (3,1 - y)

Let x1 and x2 be two different solutions of the following linear equation system. Here, if x1 = (1,1,-3,1), x2 = x1 + xd, find all xd where C^Tx2 - C^Tx1 = 1 However, c^T = [1 1 2 1].

1. Solve the system x' = 3x - 4y + 4t, y'= 4x - 7y + 7t + 1.

find x and y if (2x+1,y)=(5x+4, -7)

2. Page 922 #4 a. Solve by hand using Gaussian elimination with matrices. Show all the matrix transformations with the explanation (row operation) beside it in your Word document. Be sure to write out you answer as x = ..., y =..., and z =. and tell what this means using a. ... the terms independent, dependent, consistent, and inconsistent as applicable. 3 Page 922 #10