Discuss the validity of the following statement about linear systems. If the num

Question

Discuss the validity of the following statement about linear systems. If the number of leftmost ones is equal to the number of variables, then the system has exactly one solution. Choose the correct choice below. A. The statement is always true, because if the number of leftmost ones is equal to the number of variables, each leftmost variable in a reduced system appears in one and only one equation and no equation contains more than one leftmost variable. 1 01 The statement is false. A counterexample is 0 11 0 01 O C. The statement is always true, because if the number of leftmost ones is equal to the number of variables, the equations for the reduced matrix are in the form x1 = a1 , X2-a2, a2,a are real numbers. , xi ai, where al D. 1 0 1 The statement is false. A counterexample is0 11 Click to selert vouur answer

Explanation / Answer

The correct choice is b)

As in the option b), 0*x+0*y=1 in the third equation, which is impossible

Now, this has two leftmost ones which equals the number of variables, hence the statement is wrong

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

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