A linear system with fewer equations than unknowns is sometimes called an underde- termined system. Prove that if an underdetermined system has a solution, then it has infinitely many solutions.
A linear system with fewer equations than unknowns is sometimes called an underde- termined system. Prove...
Solving a 2x2 system of linear equations that is inconsistent or... Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. O The system has no solution. The system has a unique solution: x + 4y - 8 = 0 -x - 4y = 8 (y= 00 The system has infinitely many solutions. They must satisfy the following equation: The system has no solution. x + 4y =...
Suppose the solutions of a homogeneous system of five linear equations in six unknowns are all multiples of one nonzero so- lution. Will the system necessarily have a solution for every possible choice of constants on the right sides of the equations? Explain.
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
7. [-12 Points] DETAILS TANFIN11 2.1.009. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x - 5y = 31 2x + 3y = -1 O one and only one solution O infinitely many solutions O no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y)...
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. x1+ax2−x3 = 2 −x1+4x2−2x3 = −5 −2x1+3x2+x3 = −4 No Solutions: Unique Solution: Infinitely Many Solutions:
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
O SYSTEMS AND MATRICES Classifying systems of linear equations from graphs from both sides of System B System System A Line 11 y=-2x+5 Line 11 yx+4 Line 1: Line 2: y=x-1 Line 2:y2-4 Line 2: x+2y-6 ms that don't con Tap oblem. This system of equations is. inconsistent O consistent dependent consistent independent This system of equations is inconsistent consistent dependent consistent independent TNS means the system has: [ - This system of equations is: inconsistent O consistent dependent O...
o. (5 points) Let AX0 be a homogeneous system of n linear equations in n unknowns that has only the trivial solution. Show that if k is any positive integer, then the system A*X0 also has only the trivial solution.
Suppose a nonhomogeneous system Ax = b consisting of five linear equations with seven unknowns has a solution with three free variables. Is it possible to change some constants on the equations' right sides to make the new system inconsistent? Explain.
Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) x − 2y + 3z = 3 2x + 3y − z = 0 x + 2y − 3z = −7 (x, y, z) = ( )