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Chapter 1: Q15E (page 39)

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

15: The systemAx鈫�=[0001]inconsistent for all 4脳3matrices A.

Short Answer

Expert verified

True, the given system of equations is inconsistent.

Step by step solution

01

Step 1:Corresponding augmented matrix

We have given that,a system of equationslets the A matrix be

aeibfjcgkdhl

Now, we have given the system.

Ax鈫�=[0001]

02

Justification of answer

Put the value of A matrix in the above equation we will get.

aeibfjcgkdhlx鈫�=0001

Now since the matrix A has 3 columns then it has a maximum of 3 pivot entry.

Also, the pivot entry not possible in the last row.

This means for any value of x鈫�the value0鈮�1

Hence, the given statement is true, because the given system is inconsistent.

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Most popular questions from this chapter

LetS(t) be the length of the tthday of the year2013 in Mumbai (formerly known as Bombay), India (measured in hours, from sunrise to sunset). We are given the following values ofS(t) :


[tS(t)4711.5741227312]

For exampleS(47)=11.5, means that the timefrom sunrise to sunset on February16is11hours and30minutes. For locations close to the equator, the functionS(t) is well approximated by a trigonometric functionof the form

S(t)=a+bcos(2蟺t365)+csin(2蟺t365)

(The period is 365 days, or 1 year.) Find this approximationfor Mumbai, and graph your solution. Accordingto this model, how long is the longest day of the year inMumbai?

Compute the products Ax in Exercises 16 through 19

using paper and pencil (if the products are defined).

17.


[123456].[78]

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What can you say about the traffic volume at the four locations indicated by a question mark? Can you figure out exactly how much traffic there was on each block? If not, describe one possible scenario. For each of the four locations, find the highest and the lowest possible traffic volume.
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