Question textLet Ax=b, b ≠ 0, be a linear system with 8 unknowns and 9 equations which has exactly one solution.Select so that the following statements are always true for this type of linear system (not just for specific choices for A and b).a) The reduced row echelon form this system Answer 1 Question 6[select: , has 8 free variables, has 7 pivots, has a row of zeros, has at least 2 rows of zeros, has a column of zeros, is an identity matrix]b) The determinant of A is equal to Answer 2 Question 6[select: , 0, a negative number, a positive number, a rational number, a non-zero number, nonsense: the matrix does not have a determinant]c) The linear system Ax=0 has Answer 3 Question 6[select: , 0, exactly 1, exactly 2, exactly 3, infinitely many] solution(s).d) The matrix A is Answer 4 Question 6[select: , invertible, not invertible, irrational, symmetric, not symmetric, diagonalizable, blue]e) The matrix A has Answer 5 Question 6[select: , seven real eigenvalues, no eigenvalues, at least one real eigenvalue, the eigenvalue 666, the eigenvalue 7]Let C be the matrix consisting of the first 8 rows of A.f) The dimensions of C are Answer 6 Question 6[select: , nxn, 8x7, 7x8, 7x7, 1x8, 8x8]g) The matrix C has Answer 7 Question 6[select: , 0 or 1, no, exactly 1, exactly 2, exactly 3, infinitely many] inverse(s)h) The determinant of C is equal to Answer 8 Question 6[select: , 0, a negative number, a positive number, a rational number, a non-zero number, a real number, nonsense: the matrix does not have a determinant]i) The linear system Cz=0 has Answer 9 Question 6[select: , no solution, at least one solution, exactly one solutions, less than two solutions, infinitely many solutions]j) The matrix CT is Answer 10 Question 6[select: , symmetric, an identity matrix, invertible, not invertible, a square matrix, diagonalizable]
