Let
be the augmented matrix for a linear system. For what values of a and b does the system have
(a) a unique solution;
(b) a one-parameter solution;
(c) a two-parameter solution;
(d) (Hint: Consider the cases when a = b = 0 and otherwise.)
Problem 1 (Linear Systems of Equations). (a) Determine the values of a for which the follow- ing system of equations have no solution, exactly one solution, infinitely many solutions (a + 2)y + (a2-4)2 = (0-2) (b) If A = 4-1 0 a 2b a a be the augmented matrix of a linear system of equations then evaluate the values of a and b for which the linear system has no solution? exactly one solution? one parameter solution? two parameter...
1. Consider the following augmented matrix of a system of linear equations: [1 1 -2 2 3 1 2 -2 2 3 0 0 1 -1 3 . The system has 0 0 -1 2 -3 a) a unique solution b) no solutions c) infinitely many solutions with one free variable d) infinitely many solutions with two variables e) infinitely many solutions with three variables
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)...
5. Consider the syst em of equations: 2x-y+z2. Set up an augmented matrix and reduce to an upper triangular matrix. 5 marks a. For which value(s) of "p" (if any) does the system not have a solution? b. For which value(s) of "p" (if any) does the system have one unique solution? For which value(s) of "p" (if any) does the system have an infinite number of solutions? c. Page 5 SPRING 2019 ASSIGNMENT FILE MATH 1057 EL 12 5....
Question 7 (1 point) Let A be an REF matrix of the augmented matrix for a system of linear equations. If the system has three variables and A has three non-zero rows, then the system has at least one solution. True False
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
a) Write the augmented matrix for the linear system that corresponds to the matrix equation AX = b b) solve the above system c) write the solution as a vector A= 0 4 5 -1 3 2 and b= 1 24 5 4 2
Write the system of linear equations from the augmented matrix. (Enter your answers in terms of x, y, and z.) 1 0-3 7 0 1 0 0 0 2 -8 0 = 7 = -8 = 0 Indicate whether there will be a unique solution. O There are zero solutions. There are infinite solutions. There is a unique solution.
Below is the augmented matrix of a linear system. The unknown is a real number. 1 2 -1 0 4 2 3 -1 -1 5 0 1 -1 1 3 3 5 -2 0 10 | 1 0 2 d Several steps in finding the RREF have been done and now the matrix looks like: [1 1 0 1 3 31 0 1 -1 -3 -1 | -6 0 0 0 2 2 4 0 0 0 0 0 1...
Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution(s) to the system, if they exist. ſi 0 0 - - 1 0 1 0 - 5 0 0 1 | 10 0 0 0 - 10 (Note: The dotted vertical line in the matrix above should be a single vertical line.) a) Ox = 1, y =...