1 (8+7 15 pts) Linear equations Consider the system of equations 1 -1 0 0 0...
(c) Consider the system of linear equations 3 1 4a -1x2, where a 2 a a+1 Determine the value(s) of a such that the system is is a scalar. (i) consistent with infinitely many solutions; (ii) consistent with one and only one solution; and (ii) inconsistent. 20 marks Solve the system when it is consistent.
(c) Consider the system of linear equations 3 1 4a -1x2, where a 2 a a+1 Determine the value(s) of a such that the system...
Question 1 (8 marks) Consider the linear system x - 2y + 2z = -1 -2x + 3y + kz=1 2x + ky + (k - 4)2 = 1 (a) For which values of k is this system (i) consistent or (ii) inconsistent? (b) Find all solutions to the system when k = -1. (c) Describe your answer to (b) geometrically.
1-1 11?? (c) Consider the system of linear equations | 3 1 40-1 | x = | 2 | , where a 2 a a+1 is a scalar. (i) 1 (ii) Determine the value(s) of a such that the system is consistent with infinitely many solutions; consistent with one and only one solution; and , (iii) inconsistent. Solve the system when it is consistent. 20 marks
2. Consider the following system of linear equations 23 1 Determine whether this system is consistent, and if it is, find the full set of solutions. Also, find the rank of the matrix of coefficients.
2. Consider the following system of linear equations 23 1 Determine whether this system is consistent, and if it is, find the full set of solutions. Also, find the rank of the matrix of coefficients.
Consider the 3-dimensional system of linear equations 1 1 1 X' = X 2 1 -1 0-1 1 (a) Find a fundamental set of solutions for this system. Note that -1 is one of the eigenvalues (b) Find the general solution, and use it to find the solution satisfying -4 X(0) 2
Consider the 3-dimensional system of linear equations 1 1 1 X' = X 2 1 -1 0-1 1 (a) Find a fundamental set of solutions for this system....
Question(9) (10 points) Consider the NON-homogeneous system of linear equations, AX b, given by: 01 2 3 89 10 113 (a) Is this set of equations consistent? (In other words, are there any solutions?) (b) If the equations are consistent, find ALL solutions x.
2) The row echelon form of a system of linear equations is given. a) Write the system of equations corresponding to the given matrix. Use x, y, z; or X1, X2, X3, X4 as variables. b) Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. 1 0 2 4 0 1 -1 2 1] 2 [1 2 317 i) 0 14 21 Lo o 03] il) 0 0 i 2 0 42] 10 1...
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. Find if the following systems of linear equations is inconsistent or consistent. If it is consistent, find the parametric solution. (a) 6 8 1 12 2 -1 -1 1/2 3/2 2 (b) -21 0 5 0 2 2 0 1/3 1/3 4 2 7 1 c) 1 3 -1 0 0 2 0 9 -30 -116 0 1 1 -4 1 -1 2. Find the inverse of matrices using Gauss-Jordan technique if it exists. (a) 1 -1 1 0...
Question 4 12 pts 1 -1 1 1 0 1 -1 (a) Consider the matrix ) = 1 0 1 3 1 -3 (i) Find the space B of all vectors b € R3 such that the linear system Jx = b is consistent 4 pts 2 3 (ii) Construct a basis for space B and hence determine its dimension. 2 pts