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Chapter 4: Q 223 (page 444)

Solve each system of equations using a matrix.

x+2y+6z=5-x+y-2z=3x-4y-2z=1

Short Answer

Expert verified

The system of linear equations doesn't have any solution.

Step by step solution

01

Step 1. Given information.

Consider the given system of equations,

x+2y+6z=5-x+y-2z=3x-4y-2z=1

02

Step 2. Write in augmented form.

The augmented matrix for the given system of equations is

1265-11-231-4-21

03

Step 3. Apply row operations.

Apply R2+R1鈫�R2and R3-R1鈫�R3,

126503480-6-8-4

Apply R23鈫�R2and R3+6脳R2鈫�R3,

126501438300012

Apply R312鈫�R3,

12650143830001

Now, the matrix is in row-echelon form.

04

Step 4. Write in system of equations.

Writing the corresponding system of equations,

x+32y+12z=6......(i)y-z=-6......(ii)0=1......(iii)

As equation (iii) is a false statement.

Therefore, it is not possible to solve and is an inconsistent system.

Hence, the system of linear equations has no solution.

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Most popular questions from this chapter

The sum of two numbers is 37.

Their difference is 9. Find the

numbers.

Solve the systems of equations by substitution.

2x+y=-43x-2y=-6

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The sum of two numbers is

-27. Their difference is -59.

Find the numbers.

Without graphing, determine the number of solutions and then classify the system of equations.

y=23x+1-2x+3y=5
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