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Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill
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Given the linear system 2x - ) =5 4x -2) = /. (a ) Delennine a particular vahle of I so

Chapter 1, Problem 15

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QUESTION:

Given the linear system

2x - y = 5

4x - 2y = t,

(a) Determine a particular value of t so that the system is consistent.

(b) Determine a particular value of t so that the system is inconsistent.

(c) How many different values of t can be selected in part (b)?

Questions & Answers

QUESTION:

Given the linear system

2x - y = 5

4x - 2y = t,

(a) Determine a particular value of t so that the system is consistent.

(b) Determine a particular value of t so that the system is inconsistent.

(c) How many different values of t can be selected in part (b)?

ANSWER:

Problem 15

Given the linear system

2x - y = 5

4x - 2y = t,

(a) Determine a particular value of t so that the system is consistent.

(b) Determine a particular value of t so that the system is inconsistent.

(c) How many different values of t can be selected in part (b)?

                                                            Step-by-step solution

Step 1 of 3

(a)

Let,

   ….(1)

is consistent.

We need to  find a real number  for which the system.

Multiplying the first equation by

 we get ,

Note that the left hand side of the second equation is twice the left hand side of the first equation. Thus, for this system to be consistent, the right hand sides of the two equations must also be in the same ratio.

Therefore, the system is consistent for .

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