5.[6pts] Consider the system of linear equations in x and y. ax+by = 0 x +...
The reduced row echelon form of a system of linear equations in x and y or in x, y and z is given. For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no solutions. [1 0 0 4 0 1 0 4 Loo 01-4] A. Unique solution: x = 4, y = 4, z = 0 B. Unique solution: x = 4, y = 4, z = -4 C....
The reduced row echelon form of a system of linear equations in x and y or in x, y and z is given. For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no solutions. 1. [ 1 0 I 0 ] [ 0 1 I 0 ] [ 0 0 I 0 ] A. No solutions B. Infinitely many solutions C. Unique solution: x=1,y=1,z=0 D. Unique solution:...
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 =...
please explain every step. thanks Consider the following system of linear equations ri (a) For what values of r and s is this system of linear equations inconsistent? (b) For what values of and s does this system of linear equations have infinitely many solutions? (ey For what values of and s does this system of linear equations have a unique solution?
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...
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
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...
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...
- Tll Find values of a, b, and a much that the system of linear equations has (i) no solution, (ii) exactly une solution, and (iii) infinitely many solutions. 0 { x + 2y = 3 1. (ax+by = -9 @ S2X - Y + Z-a 1 x + y +22=b | 3x + 37=C.
2 x [b] Consider the following linear system of equations AX =B : (i) Determine a basis for the row space of A. (ii) Compute the Rank of the augmented matrix (A:B), then use it to classify the solution of this system (Unique - Many -No: solution). (iii) Is the matrix A diagonalizable? Explain your answer and verify the similarity transformation.