Q3Comprehension1.5 Marks22 Dec 2024PassageLet A = [1−1k111513]\begin{bmatrix} 1 & -1 & k \\ 1 & 1 & 1 \\ 5 & 1 & 3 \end{bmatrix}115−111k13 where k in R. Answer the given subquestions.If k = 1 and b = [0, 2, α\alphaα]^T, then which of the following options is true?AIf α\alphaα = 5, then the system Ax = b will have a unique solution.BIf α\alphaα = 6, then the system Ax = b will have infinitely many solutions.CIf α\alphaα = 5, then the rank of the augmented matrix [A | b] is not equal to rank of A.DIf α\alphaα = 6, then b does not belong to the column space of A.
