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Chapter 1: Q19E (page 1)

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

19. There exits a matrix A such thatA[-12]=[357]

Short Answer

Expert verified

It is true that there exists a matrix A such thatA[-12]=[357]

Step by step solution

01

Step 1:Assuming the matrix 

Since, the order of matrix A should be 3脳2

Let the matrix A be

abcdef

02

Justification of answer  

Now put the value of Matrix A in the given equation we get.

abcdef-12=357

Now after solving the above equation we get.

-a+2b=3-c+2d=5-e+2f=7鈬�b=3+a2,d=5+c2,f=7+e2

The A matrix will become

a3+a2c5+c2e7+e2

Hence, it is true that there exists a matrix A such thatA[-12]=[357]

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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?

The reduced row-echelon forms of the augmented matrices of three systems are given here. How many solutions does each system have?

a.[102|013|000|001]b.[10|501|6]c.[010|2001|3]

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

18:[111315171921][-13-1]=[131921]

Consider the accompanying table. For some linear systemsA=x鈫�=b鈫�, you are given either the rank of the coefficient matrixA , or the rank of the augmented matrix [A:b鈫�]. In each case, state whether the system could have no solution, one solution, or infinitely many solutions. There may be more than one possibility for some systems. Justify your answers.

Solve the linear system of equations. You may use technology.

|3X+6y+14z=227X+14y+30z=464X+8y+7z=6|
See all solutions

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