Chapter 11: Q. 22 (page 793)

In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 2 x + y + z = 5 \\ 4 x - y - 3 z = 1 \\ 8 x + y - z = 5 \end{array}$

Short Answer

Expert verified

The system of equations has no solution or the equations are inconsistent.

Step by step solution

Step 1. Given information

The given system of equations is $\{\begin{array}{r} 2 x + y + z = 5 \\ 4 x - y - 3 z = 1 \\ 8 x + y - z = 5 \end{array}$

Step 2. Solve system of equations using matrix

$A = [\begin{array}{ccc} 2 & 1 & 1 \\ 4 & - 1 & - 3 \\ 8 & 1 & - 1 \end{array}], X = [\begin{array}{l} x \\ y \\ z \end{array}], B = [\begin{array}{l} 5 \\ 1 \\ 5 \end{array}]$

$A X = B X = A^{- 1} B$

The inverse of the matrix $A$ does not exist. Therefore, the system of equations has no solution or the equations are inconsistent.

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In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 2 x + y + z = 5 \\ 4 x - y - 3 z = 1 \\ 8 x + y - z = 5 \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

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In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.2x+y+z=54x−y−3z=18x+y−z=5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 2 x + y + z = 5 \\ 4 x - y - 3 z = 1 \\ 8 x + y - z = 5 \end{array}$