Given thatA = 3 4 −2 −5 12 16 −8 −206 8 −4 −10 and b = b1 b2b3find the row echelon form of the augmented matrix [A | b]. b1 b1 + b2 b1 + b3Therefore, the system Ax = b is consistent when b satisfies the following restrictions. (Enter your answers as equations in terms of b1 and b2, and in terms of b1 and b3.)equation in terms of b1 and b2      equation in terms of b1 and b3

Given the following, find the reduced row echelon form of the augmented matrix [A | b]. (Enter your answer as one augmented matrix.)A = 2 2 6 14 4 4 15 34 and b = 16 38RREF = Find the solution of Ax = b, where s and t are arbitrary real numbers. (Assume x2 = s and x4 = t. If a solution does not exist, enter DNE into any cell of each matrix.)

1. Systems of linear equations(a) Consider the following system of linear equationsz − 4w = −4y − 3z + 14 = 133x + z + w = 1x + w = 2.Determine whether or not the system is consistent, and if it is, give a particular solution.[10 Marks](b) Compute the reduced row echelon form of the matrix0 0 1 1 11 3 −2 0 −12 6 −3 1 0 .[5 Marks]Suppose a system of linear equations is represented as an augmented matrix with reduced row echelon form1 0 4 00 1 1 00 0 0 10 0 0 0 .(c) Is the system consistent?[5 Marks](d) Give a basis for the solution set of the corresponding homogeneous system.[5 Marks][End of Question 1: Total 25 marks]COMP1043-MOCK Turn over

Given the corresponding augmented matrix of a system, determine whether the system is consistent.[−411ln3−232(−1+πcos5π2)1][−41−22(−1+𝜋cos⁡5𝜋2)1ln⁡331]Answer files

[Linear Algebra] 6. For which conditions on b = (b1, b2, b3, b4) do there exist solution(s) for the linear system Ax = b? (a) A = [ 2 4 1 8 / 4 8 2 10 / 1 2 0 3 / 8 10 4 14] (b) A = [2 2 2 2 2 2 / 4 4 2 4 6 6 / 1 2 2 0 1 1 / 8 8 8 8 8 8]

If the row echelon form is not strictly triangular, then the system may also have an unique1solution.