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Chapter 4: Q 224 (page 444)

Solve each system of equations using a matrix.

x+2y-3z=-1x-3y+z=12x-y-2z=2

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

Step 1. Given information.

Consider the given system of equations,

x+2y-3z=-1x-3y+z=12x-y-2z=2

02

Step 2. Write in augmented form.

The augmented matrix for the given system of equations is

12-3-11-3112-1-22

03

Step 3. Apply row operations.

Apply R2-R1鈫�R2and R3-2脳R1鈫�R3,

12-3-10-5420-544

Apply R2-5鈫�R2and R3鈫�R3+5脳R2,

12-3-101-45-250002

Apply R32鈫�R3,

12-3-101-45-250001

Now, the matrix is in row-echelon form.

04

Step 4. Write in system of equations.

Writing the corresponding system of equations,

x+2y-3z=-1......(i)y-45z=-25......(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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