a. The echelon form of a matrix is unique. Choose the correct answer below. 0 A.

Question

a. The echelon form of a matrix is unique. Choose the correct answer below. 0 A. The statement is false. Both the echelon form and the reduced echelon form of a matrix are unique. They are the same regardless ofthe chosen row operations O B. The statement is false. The echelon form of a matrix is not unique, but the reduced echelon form is unique. ° C. The statement is true. Neither the echelon form nor the reduced echelon form of a matrix are unique. They depend on the row operations performed. O D. The statement is true. The echelon form of a matrix is always unique, but the reduced echelon form of a matrix might not be unique b. The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. Choose the correct answer below. ( A. O B. ° C. 0 D. The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix. The statement is true. The pivot positions in a matrix are determined completely by the positions of the leading entries of each row which are dependent on row interchanges. The statement is true. Every pivot position is determined by the positions of the leading entries of a matrix in reduced echelon form The statement is false. The pivot positions in a matrix depend on the location of the pivot column. C. Reducing a matrix to echelon form is called the forward phase of the row reduction process. Choose the correct answer below 0 A. O B. ? C. 0 D. The statement is true. Reducing a matrix to echelon form is called the forward phase and reducing a matrix to reduced echelon form is called the backward phase. The statement is true. The forward phase occurs when a linear system has both basic and free variables, which can only be determined by reducing a matrix to echelon form. The statement is false. The forward phase does not depend on whether a matrix is in echelon form or reduced echelon form. The statement is false. Reducing a matrix to echelon form is called the backward phase and reducing a matrix to reduced echelon form is called the forward phase

Explanation / Answer

a) The echelon form of a matrix is formed by the rows with zero below the leading entries and it is not unique.where as reduced echelon form is unique. So the given statement is false.the option B is correct answer.

b) the pivot positions in a matrix are uniquely determined and does not depends on whether row interchanges used.the given statement is false.so from the given options A is the correct answer.

c)the forward phase produces a row echelon form the

input matrix and from this echelon form backward phase produces reduced row echelon form. So the given statement is true.from the options given A is the correct answer.

d) the given statement is false. For example consider augmented matrix x1+x2=1 ,x1+x2=2 has the reduced echelon form with x2 as a free variable,but is inconsistent. So option C is the correct answer.

e) the given statement is true and the option A is the correct answer.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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