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Decide whether the following systems are singular or nonsingular, and whether they have

Chapter 1, Problem 1.5.18

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QUESTION:

Decide whether the following systems are singular or nonsingular, and whether they have no solution, one solution, or infinitely many solutions: v w = 2 u v = 2 u w = 2 and v w = 0 u v = 0 u w = 0 and v + w = 1 u + v = 1 u + w = 1.

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QUESTION:

Decide whether the following systems are singular or nonsingular, and whether they have no solution, one solution, or infinitely many solutions: v w = 2 u v = 2 u w = 2 and v w = 0 u v = 0 u w = 0 and v + w = 1 u + v = 1 u + w = 1.

ANSWER:

Step 1 of 3

Given system of linear equations is

The coefficient matrix is

Now,

Since , the system is singular and has either no solution or infinitely many solutions.

Now,

Since and the system has no solution.

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