Answer the questions below relating to linear algebra (three parts). Please make sure to easily/accurately answer all the question parts.

Find the general solution of the system whose augmented matrix is given below. - -50 -1 0 -4 60 10 0 -3 2 0 00 1 6 5 0 00 0O 0 O () Select the correct choice below and, if necessary, fill in the answer boxes to complete your answer. O A. O B. ( C. O D. x1= b x = ioonaetertl, X, Is free X = Xo =|:| X3 = X5 Is free X3 is free x4 is free X, = x4=|:| X Is free X5 = Xg is free Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. Choose the correct answer below. O A The system is consistent because the augmented matrix will contain a row of the form [ 0 --0b } with b nonzero. () B. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix. () C. The system is consistent because all the columns in the augmented matrix will have a pivot position. D. The system is consistent because the rightmost column of the augmented matrix is not a pivot column. Determine if b is a linear combination of the vectors formed from the columns of the matrix A. 1 -4 2 4 A= 0 6 7 [b=| -7 -3 12 -6 -4 Choose the correct answer below. () A. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column and the third entry in the second column, and the third entry in the third column. () B. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column. () C. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column. () D. Vector b is not a linear combination of the vectors formed from the columns of the matrix A