Which one of the following is true? a) In a reduced echelon form, using different row operations, a matrix can be reduced to more than one matrix. b) Only the augmented matrices are applicable for the row reduction algorithm. c) A solution set contains infinitely many solutions if is has free variables. d) The variable that corresponds to the pivot column in the coefficient matrix is a basis variable

Please solve for P* Q* and v   11.3 3

Is it possible that all solutions of a homogeneous system of twelve linear equations in fourteen variables are multiples of one fixed nonzero solution? Discuss. Consider the system as Ax = 0, where A is a 12x 14 matrix. Choose the correct answer below. O A. Yes. Since A has at most 12 pivot positions, rank As 12. By the Rank Theorem, dim Nul A = 14- rank Az 2. Since there is at least one free variable in the system, all solutions are multiples of one fixed nonzero solution. O B. No. Since A has 12 pivot positions, rank A= 12. By the Rank Theorem, dim Nul A = 12 - rank A= 0. Since Nul A = 0, it is impossible to find a single vector in Nul A that spans Nul A. OC. No. Since A has at most 12 pivot positions, rank As 12. By the Rank Theorem, Nul A= 14 - rank Az 2. Thus, it is impossible to find a single vector in Nul A that spans Nul A. O D. Yes. Since A has 12 pivot positions, rank A= 12. By the Rank Theorem, dim Nul A= 12- rank A= 0. Thus, all solutions are multiples of one fixed nonzero…

Solve the following systems of equations using a valid elimination algorithm, include all the elementary line operations that you used to solve it, then check that your result is correct, using another method (it can be computational). Write the solution vector. note: Do everything that is asked above (in the image are the equations and the matrix)