For which values of a, is 0 (Hint:Find all a such that the linear system with...
2. (a) The linear system 212 + bıy+cı2 = 0 02.2 + b2y + 0,2 = 0 232 + b3y + c32 = 0 has infinitely many solutions, i. (3 marks) What can you say about the number of solutions of the following system? Explain. 412+by+C12 = 3 22x + b2y + C22 azx + b3y + C32 11 = 7 bi ii. (3 marks) Is the set W b2 linearly independent? b3 Explain. (b) (4 marks) The augmented matrix...
3. (6 marks) For b1,b2, 63, 64 € R, consider the linear system of equations + 21 + 22 -11 + 22 23 624 = bi 3.13 + 2014 b2 23 + 2:04 b3 603 + 20:24 = 54 *) 21 + 2:01 + 4.22 where 11, 12, 13, 14 ER. (a) Find a system of equations that bı, b2, 63, 64 must satisfy in order for (+) to be consistent. bi [ must satisfy so (+) is (b) Using...
2. (a) The linear system 0 212 +by+C12 02x + b2y +0.2 23.C + b3y + 232 0 = 0 0 has only the zero solution 0 i. (3 marks) Determine the number of solutions of the following system. Explain. 212 + by + C2 = 3 02.2 + b2y + 0,2 = 7 03.2 + b3y + 232 11 bi ii. (3 marks) Is the set W b linearly independent? b3 Explain. (b) (4 marks) The augmented matrix for...
I
Undertand how the first two rows came about in the matirx, but I
dont underatnd how the last row was calculated. How did it go from
-4b1 +b3 to -2b1-b2+b3
Problem 5. (20) Find conditions(s) on bi, bz and by in order to guarantee that the linear system 13 consistent *+y-2=b 2x - 4y + 5z = b2 4x - 2y + 3z = b3 Solution. We use the augmented matrix and reduce the system. 11 1 -16] [1...
- Consider the matrix equation At = b given by the system 11 2 11 21 + 2:12 + 4.12 + 2.62 13 - 314 = b + 204 = by 13 + 5x4 = 63 + a) Write down the corresponding augmented matrix ( Ab) and use row operations to transform it into a matrix of the form (A b') where the coefficient matrix A' is in reduced row echelon form. (That is, you don't need to put the...
Matrix Algebra
Consider the traffic flow diagram that follows, where a1, az, a3, 24, 61, 62, 63, 64 are fixed positive integers. Set up a linear system in the unknowns X1, X2, X3, X4 and show that the system will be consistent if and only if a1 + a2 + a3 + 24 = 61 + b2 + b3 + 64 What can you conclude about the number of automobiles entering and leaving the traffic network? ai ba bi X1...
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...
of the linear system whose augmented matrix is the matrix (b) Find all solutions (in vector form ſi 0-5 -6 0 77 B = 0 1 4 -1 0 2 . 0 0 0 0 1 -3
plz help me with this one and explain each step
Determine the value(s) of h such that the matrix is the augmente d matrix of a consistent linear system. -2 89 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The matrix is the augmented matrix of a consistent linear system if h O B. The matrix is the augmented matrix of a consistent linear system if h (Use a...
Convert the given linear system to an augmented matrix and then find all solutions. Write the solutions in parametric form. 2x1 + 6x2 − 9x3 − 4x4 = 0 −3x1 − 11x2 + 9x3 − x4 = 0 x1 + 4x2 − 2x3 + x4 = 0