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Chapter 3: Q20P (page 123)

solve the set of equations by the method of finding the inverse of the coefficient matrix.

{2x+3y=-15x+4y=8

Short Answer

Expert verified

The solution of the given set of equations is x=4 and y=-3 .

Step by step solution

01

Definition of inverse of a matrix:

The inverse of a matrix M is defined as the matrix M-1 such that MM-1 and M-1M are both equal to a unit matrix I .

02

 Find the inverse of the matrix:

The given set of equations are

2x+3y=-15x+4y=8

The solution is to be found by the method of finding the inverse of the coefficient matrix. Here,

M=2354

So,

C=C11C12C21C22=4-5-32

Find inverse of matrix M .

M-1=1detMCT=14×2-3×54-3-52=17-435-2

03

 Find the solution of equations:

Use equation M-1k=rto solve the equations, where is the matrix of coefficient and is the unknown vector. Here, k=-18 and r=xy .

17-435-2-18=xy1728-21=xy4-3=xy

Therefore, x=4 and y=-3 .

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Most popular questions from this chapter

Find AB,BA,A+B,A-B,A2,B2,5-A,3-B. Observe thatAB≠BA.Show that(A-B)(A+B)≠(A+B)(A-B)≠A2-B2. Show that det(AB)=det(BA)=(detA)(detB), but that det(A+B)≠detA+detB. Show that det(5A)≠5detA and find n so that localid="1658983435079" det(5A)=5ndetA.Find similar results for det(3B). Remember that the point of doing these simple problems by hand is to learn how to manipulate determinants and matrices correctly. Check your answers by computer.

localid="1658983077106" A=(25-13),B=(-1402)

Find AB, BA , A+B , A-B , A2, B2,5.A,3,B . Observe that AB≠BA. Show that (A-B)(A+B)≠(A+B)(A-B)≠A2-B2. Show that det(AB)=det(BA)=(detA)(detB), but that det(A+B)≠detA+detB. Show that det(5A)≠5detA and find n so that det(5A)=5ndetA. Find similar results for det(3B). Remember that the point of doing these simple problems by hand is to learn how to manipulate determinants and matrices correctly. Check your answers by computer.

role="math" localid="1658986967380" A=(1023-10051),B=(1100213-10)

the determinants in Problems 1 to 6 by the methods shown in Example 4. Remember that the reason for doing this is not just to get the answer (your computer can give you that) but to learn how to manipulate determinants correctly. Check your answers by computer.

In Problems8to15,use (8.5) to show that the given functions are linearly independent.

1,x2,x4,x6

In Problems 8 to 15,use to show that the given functions are linearly independent.

15.ex,eix,cosh⁡x
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