Suppose M is the augmented coefficient matrix for a system of equations augmente

Question

Suppose M is the augmented coefficient matrix for a system of equations augmented by the constants of the equations. We'll say that an operation is allowable if we can apply it to M and produce the augmented coefficient matrix for a system of equations with the same solution as the original system of equations:these correspond to the steps you use to solve a system of equations. For each of the following identify the corresponding operation on a system of equations:then state whether the operation is allowable or forbidden. Assume c notequalto 0. Multiplying every term of a row by c. Switching two columns. Switching two rows. Adding c to each term in a row. Multiplying every term in a row by c, then adding the corresponding terms to another row. Suppose that, after you've applied a sequence of allowable row operations to M, you end up with a row consisting of all zeroes except the last entry, which is a non-zero number. What does this say about the original system of equations?

Explanation / Answer

2(a). Multiplying every term of a row by a constant c is an allowable operation as the entire related equation gets multiplied by c. This has no effect on the equation/solution to the system of equations.

(b). Switching 2 columns ( not involving the column comprising the constant terms on the right hand side of the equations) has the effect of interchanging the related variables. There, this is not an allowable operation, unless, a similar change is made in the solution to the system of equations. If the column of constant terms is switched with another column, the solution gets affected. Therefore, this is not an allowable operation.

(c ). Switching 2 rows is an allowable operation as this simply results in interchange of the related equations. This has no effect on the solution to the system of equations.

(d).Adding c to each term in a row is not an allowable operation as this changes the related equation.

( e). Multiplying every term of a row by a constant c and then adding the corresponding terms to another row is an allowable operation as this does not have any effect on the system of equations.

(f). If after applying a sequence of allowable row operations , we end up with a row of zeros except the last entry, which is non-zero, then the given system of equations ins inconsistent.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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