PLEASE! I need your HELP! These are problems from my Linear Algebra class: a. Su

Question

PLEASE! I need your HELP! These are problems from my Linear Algebra class:

a. Suppose A is the augmented matrix of a system of linear equations in n variables and that B is a row-equivalent matrix in reduced row-echelon form with r pivot columns. If r = n + 1, prove that the system of equations is inconsistent.

b. Suppose that the coefficient matrix of a consistent system of linear equations has two columns that are identical. Prove that the system has infinitely many solutions.

d. Suppose a homogeneous system of equations has 13 variables and 8 equations. How ?many solutions will it have? Why? ?

e. Prove or disprove: A system of linear equations is homogeneous if and only if the system has the zero vector as a solution.

Explanation / Answer

a) If r = n+1, then no of pivots are more than the no of variables. Hence unique solution not possible thus inconsistent.

b)Ax =B has unique solution only if matrix A is non singular.

Since here A has two identical rows it is singular, but since given to be consistent there is an infinite number of solutions.

c)

d) 8 equations and 13 variables cannot have unique solutions. They have infinitely dependent solutions

e)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.