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Chapter 1: Q47E (page 40)

Determine whether the statements that follow are true or false, and justify your answer.

47.If ad-bc鈮�0, then the matrix(abcd) must have rank 2.

Short Answer

Expert verified

The statement, ad-bc鈮�0鈥淚f , then the matrix abcdmust have rank 2 .鈥� is false.

Step by step solution

01

Consider the condition

Consider the matrix.

abcd

The reduced row-echelon form of the matrix is,

ab0d-bca

Thus, the condition is, a鈮�0.

02

Conclusion

Hence, for the matrix abcd to have a rank of 2 , the condition to be satisfied is, a鈮�b.

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Most popular questions from this chapter

Question:A linear system of the formAx鈫�=0 is called homogeneous. Justify the following facts:

a.All homogeneous systems are consistent.

b.A homogeneous system with fewer equations than unknowns has infinitely many solutions.

c.Ifx1鈫�andx2鈫� are solutions of the homogeneous systemAx鈫�=0, thenx1鈫�+x2鈫� is a solution as well.

d.Ifx鈫� is a solution of the homogeneous systemAx鈫�=0 andkis an arbitrary constant, thenkx鈫� is a solution as well.

If you sell two cows and five sheep and you buy 13 pigs, you gain 1000coins. If you sell three cows and three pigs and buy nine sheep, you break even. If you sell six sheep and eight pigs and you buy five cows, you lose600 coins. What is the price of a cow, a sheep, and a pig, respectively? (Nine Chapters, Chapter 8, Problem 8)

The system is[123456000]x鈫�=[123]inconsistent

Determine whether the statements that follow are true or false, and justify your answer.

17: Rank|222222222|=2

In Exercises 1 through 12, find all solutions of the equations

with paper and pencil using Gauss鈥揓ordan elimination.

Show all your work.

|x1+2x3+4x4=-8x2-3x-x4=63x1+4x2-6x3+8x4=0-x2+3x3+4x4=-12|
See all solutions

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