Write the system of linear equations in the form Ax = b and solve this matrix equation for x. = 9 -X1 + X2 -2x1 + x2 = 0 (No Response) (No Response) X1 1- [:)] (No Response) (No Response) X2 (No Response) X1 X2 (No Response)
Write the system of linear equations in the form Ax = b and solve this matrix equation for x. x1 – 2x2 + 3x3 = 24 -X1 + 3x2 - x3 = -11 2x1 – 5x2 + 5x3 = 42 X1 x2 = X3 ] 24 -11 42 [ x
4 Given Ax = b 2 4 6 4 bi 4 A=12576 23 5 2 b3 1. Reduce [A b]to [U cl,so that Aa b becomes a triangular system Ux-c. 2. Find the condition on b1, b2, bs for Aabto have a solution. 3. Describe the column space of A. Which plane in R3? 4. Describe the nullspace of A. Which special solutions in R4? 5. Reduce [U c]to[R d]: Special solutions from R, particular solution from d. 6. Find...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaussian elimination and express the general solution in vector form. (b) (5 points) Write down the corresponding homogenous system Ax-0 explicitly and determine all non-trivial solutions from (a) without resolving the system
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by...
Write the following system of equations in the form AX = B, and
calculate the solution using the equation
x + y = -6
3x - y = -2
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5.[6pts] Consider the system of linear equations in x and y. ax+by = 0 x + dy = 0 (a) Under what conditions will the system have infinitely many solutions? (6) Under what conditions will the system have a unique solution? (c) Under what conditions will the system have no solution?
1. (20 points total) We will solve the following system of linear equations and express the problem and solution in various forms. 2x1 + 4x2 + x4 – 25 = 1 2.22 - 3.23 – 24 +2.25 = 1. (a) (2 point) How many free parameters are required to describe the solution set? (b) (5 points) Write the problem in the form of an augmented matrix and use Gauss-Jordan elimination to find the reduced echelon form of the matrix. (c)...
5. Given the system of equations (92 – X – 5y + 7 = 0 x – y + 32 – 1 = 0 2x + y = 5 = a. Write the system in the matrix form AX b. [1 points] b. Write out the augmented matrix for this system and calculate its row-reduced echelon form. [2 points] c. Write out the complete set of solutions. [2 points]
Iry to hhel ieal 4 Suppose that the 3 x 2 matrix A has rank 2 and we want to solve Ax b. a) (10 pts) If there exists a solution x ()l show that 0 0 b) (5 pts) Is the 3 x 3 augmented matrix (Alb) invertible? Why or why not? c) (10 pts) Suppose that you found the solution below 2 (A | b) 30 0 Can you compute the solution to Ax = b? If yes...
Problem 1. For the system of linear equations Ax- b, using elementary row operations on the augmented matrix, A is brought to row echelon form. The resulting augmented matrix is: 1 0 7 0 112 Row echelon form of (Alb-00 1 2 3 5 0 0 0 0 0 c (a) Find the rank and the nullity of A. Explain your answer. (b) For what values of c does the system have at least one solution? Explain your answer. (c)...