1. Consider the system of equations given by: 2x + 4y + 6z = 18 4x + 5y + 6z = 24 2x + 7y + 12z = 30. (a) Solve the linear system above by writing the system as an equivalent augmented matrix, and by then putting this augmented matrix in row echelon or reduced row echelon form. Explicitly state the values of x, y, and z that make the equations above true. Identify which variables are free variables if there are any. (b) Do the columns of B = 2 4 4 5 span R3? Why or why not? 2 7 12 (c) Find a column vector 7 = such that all of the solutions of the matrix equation Ba = 0 are scalar multiples of the vector U. ( a ) . -2 4 6 187 4 5 6 24 2 3 4 56 2.7 12/ 30 SX- 1 =1 X= 1+z y + 22 = 4 y= 4- 22 2 is free variable b ) . 4 6 4 56 ... 012 -2 7 12 0 0 0 Two pivots is it doesn't span RS