[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]

[Linear Algebra] 8. Let A = [2 1 6 1 / 3 1 7 2 / 4 1 8 3 / 5 1 9 3] (a 4x4 matrix), b = [1 1 k 4] (a 4x1 matrix). (a) Find condition on k ∈ R such that Ax = b, x ∈ R4 is solvable. (b) When the solution exists, find all solutions.

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

Solve the system Ax=b, where A=\left[\begin{array}{ccc} 3&4\\ {5}&{6}\end{array}\right] and b=\left[\begin{array}{ccc} 5.2\\ {7}\end{array}\right]. What value is the first entry of x?

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.)

Construct a 2 × 2 matrix A such that the solution set of the equationAx = 0 is the line in R2 through (4, 1) and the origin. Then, find a vectorb in R2 such that the solution set of Ax = b is not a line in R2 parallelto the solution set of Ax = 0.